Quiz5-7_Solutions

xlsx

School

Ohio State University *

*We aren’t endorsed by this school

Course

MISC

Subject

Finance

Date

Jan 9, 2024

Type

xlsx

Pages

41

Uploaded by MajorBraveryRhinoceros25

Report
QUIZ 5 - Q1 u 1.4 42 d 0.8 7 1+rf 1.1 stock 30 K 35 call 3.18 24 p 50.00% 0 1-p 50.00% Δ 0.389 B -8.485 P=C+PV(K)-S 5.00 QUIZ 5 - Q2 u 1.5 75 d 0.7 0 1+rf 1.0050 stock 50 K 60 put 15.39 35 p 38.13% 25 The price of a stock can go up by 40%, or down by 20% over the next year (so, u=1.4 and d=0.8). The an The current value of the stock is $30. You need to price a call option with one year maturity and strike p What is the number of shares of the stock Δ in the replicating portfolio of the call option? What is the number of risk-free bonds B (priced today at $1) in the replicating portfolio of the call optio What is the current price of the call option? What is the risk-neutral probability p that the stock will go up by 40% over the next year? Using the put-call parity without dividends, what is the price of a put option with one year maturity and The price of a stock can go up by 50%, or down by 30% over the next month (so, u=1.5 and d=0.7). The 6.17%. The current value of the stock is $50. You need to price a put option with one month maturity a What is the number of shares of the stock Δ in the replicating portfolio of the call option? What is the number of risk-free bonds B (priced today at $1) in the replicating portfolio of the call optio What is the current price of the put option? What is the risk-neutral probability p that the stock will go up by 50% over the next year? Using the put-call parity without dividends, what is the price of a call option with one month maturity a
1-p 61.87% Δ -0.625 B 46.642 C=P+S-PV(K) 5.69 QUIZ 5 - Q3 u 1.1 27.5 d 0.9 144.26 1+rf 1.0030 stock 25 derivative 125.71 22.5 p 51.48% 106.80 1-p 48.52% pi_u 0.513 pi_d 0.484 QUIZ 6 - Q1 T 0.5 518.40 n 3 432.00 sigma annual 44.66% 360.00 360.00 stock 300 300.00 u 1.20 250.00 250.00 d 0.83 208.33 173.61 The price of a stock can go up by 10%, or down by 10% over the next two weeks (so, u=1.1 and d=0.9). is 8%. The current value of the stock is $25. What is the risk-neutral probability p that the stock will go up by 10% over the next two weeks? What is the state price pi_u? What is the state price pi_d? What is the value of a derivative with payoff in two weeks of SQRT(ST^3+15), where ST is the price of th Write down the dynamics of the stock price in the following 3-period binomial model (n=3), by first det and d responsible for the proportional changes of the stock price. The annual volatility of the stock pric time to expiration T is 6 months.
QUIZ 6 - Q2 T/n 0.0192307692 sigma annual 62.14% 1+rf 1.0008 u 1.09 d 0.92 p 48.32% QUIZ 6 - Q3 T 0.0385 203.13 n 2 0.00 1+rf 1.00112 162.50 u 1.25 11.05 d 0.8 stock 130 130.00 K 150 put 30.25 20.00 104.00 p 44.69% 45.83 1-p 55.31% 83.20 66.80 QUIZ 7 - Q1 Consider a stock price with annual volatility sigma of 62.14% and an annual risk-free rate of 4.3%. What neutral probability p that the stock will go up in a binomial model where the stock price changes propo value and each period corresponds to one week? Consider the following evolution of the price of AMZN in the next two weeks, where the stock price cha previous value with u=1.25 and d=0.8. Given an annual risk-free rate of 6%, determine the price of a Eu AMZN that expires in 2 weeks and has a strike price K = 150. It is never optimal to exercise early an American Call option on a stock that is expected to pay dividend date. - True - False
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
QUIZ 7 - Q2 QUIZ 7 - Q3 T 0.0385 203.13 n 2 0.00 1+rf 1.00112 162.50 u 1.25 11.05 d 0.8 stock 130 130.00 K 150 put 30.35 20.00 104.00 p 44.69% 46.00 1-p 55.31% 83.20 66.80 QUIZ 8 - Q1 Which of the following statements is false? - American options are in general more expensive than European options - It is not possible to price an American option without having determined the optimal exercise strategy - The time value of an American option can be negative - The put-call parity holds in general only for European options Consider the following evolution of the price of AMZN in the next two weeks, where the stock price cha previous value with u=1.25 and d=0.8. Given an annual risk-free rate of 6%, determine the price of a Eu AMZN that expires in 2 weeks and has a strike price K = 150. For which of the following possible times/states before expiration it is optimal to exercise early? - time 0 - time 1u - time 1d Calls are equivalent to long positions in the underlying asset financed with borrowing. As the underlyin more of the stock (with borrowed money), whereas as the underlying asset goes down we sell (and liqu - True - False
QUIZ 8 - Q2 QUIZ 8 - Q3 Black-Scholes calculator Asset price 40.00 40.00 1+r_f 1.05 1.05 Strike 40.00 40.00 x 0.3126 0.4421 Time 1.00 2.00 N(x) 0.6227 0.6708 Risk-free return 5.00% 5.00% N(x2) 0.5050 0.5071 Divident yield 0.00% 0.00% N'(x) 0.3799 0.3618 Volatility 30.00% 30.00% Call price 5.6692 8.4329 Put price 3.7644 4.7141 Delta call 0.6227 0.6708 Delta put (0.3773) (0.3292) Puts are equivalent to short positions in the underlying asset coupled with lending. As the underlying a of the stock (with our lent money), whereas as the underlying asset goes down we sell more (lending it - True - False Assume the current price of a non-dividend paying stock is $40, and the term structure is flat with a dis stock under consideration has an expected return of 15%, and a volatility of 30%. According to the Black-Scholes model, what should be the price of a call option on the stock with a strik maturity? According to the Black-Scholes model, what should be the price of a call option on the stock with a strik maturity?
Gamma 0.0317 0.0213 Theta call (3.2182) (2.4327) Theta put (1.3595) (0.6625) Vega 15.1966 20.4662 QUIZ 8 - Q4 Black-Scholes calculator Asset price 10.00 Delta 0.5236 1+r_f Strike 11.00 Cash -3.96003175 x Time 1.00 N(x) Risk-free return 5.00% N(x2) Divident yield 0.00% N'(x) Volatility 37.00% Call price 1.2763 Put price 1.7525 Delta call 0.5236 Delta put (0.4764) Gamma 0.1076 Theta call (0.9300) Theta put (0.4188) Vega 3.9824 QUIZ 8 - Q5 Assume the current price of the SPZ is $10, and the term structure is flat with a discount rate of 5% in t expected to appreciate by 15%, and it has a volatility of 37%. Assume SPZ pays no dividends. According to the Black-Scholes model, what should be the price of a call option on the SPZ with a strike maturity? According to the Black-Scholes model, what is the replicating portfolio of the above call? Express it in te SPZ, and a cash position (in US dollars). Assume the price of Telsa's stock is $10, and that a call option on Tesla with a strike of $10 and a 1 year Assume the risk-free rate is 5%, and that Tesla pays no dividends. Estimate the volatility of Telsa.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Asset price 10.0 1+r_f 1.05 Strike 10.0 x 0.4290 Time (years) 1.00 N(x) 0.6660 Risk-free return 5.00% N(x2) 0.3843 Dividend yield 0.00% N'(x) 0.3639 Volatility 72.31% Call price 3.0000 Put price 2.5238 QUIZ 9 - Q1 No options (calls) 10.0 5.0 Delta-hedging Asset price 100.0 100.0 100.0 Delta_POR Strike 100.0 110.0 97.0 x Your firm holds in its balance sheet 10m call options with a strike of K=100, and 5m options with a strike of K=110. Both sets of options have a 3 year maturity. The und asset of the options is SloppySoft Inc, that you estimate has a volatility of 83%, and expected to appreciate by more than 50% over the next 3 years. SloppySoft Inc’s closi at the NYSE today is $100. The firm pays no dividends. Assume the risk-free rate is a 0%. (a) Estimate the value of the options using the Black-Scholes model. Each call option with K = 100 is worth 52.77, and each option with K = 110 is wo 50.51. So the total portfolio is wroth about $780m. (b) According to the Black-Scholes model, what would be the price of the options if pySoft Inc’s price went down to $99? The options would go down in value to $52.01 and $49.77, so the total portfolio v would be $769m, for a loss of −11.3m. (c) What is the Black-Scholes Delta of SloppySoft Inc’s options portfolio? The Delta is given by ∆ = 10(0.76) + 5(0.74) = 11.4 (d) If you wanted to be delta neutral, what trade in SloppySoft Inc’s stock would you s Shorting 11.4m units of SloppySoft Inc’s stock would make the portfolio delta-neu
Time (years) 3.00 3.00 0.25 Risk-free return 0.00% 0.00% 0.00% Dividend yield 0.00% 0.00% 0.00% Volatility 83.00% 83.00% 83.00% 1+r_f 1.00 1.00 1.00 Delta_new x 0.7188 0.6525 0.2809 Gamma_new N(x) 0.7639 0.7430 0.6106 N(x2) 0.2361 0.2162 0.4467 N'(x) 0.3081 0.3224 0.3835 Call price 52.7737 50.5144 17.7345 Put price 52.7737 60.5144 14.7345 Delta call 0.7639 0.7430 0.6106 Delta put (0.2361) (0.2570) (0.3894) Gamma 0.0021 0.0022 0.0092 QUIZ 9 - Q2 Your firm holds in its balance sheet 10m call options with a strike of K=100, and 5m options with a strike of K=110. Both sets of options have a 3 year maturity. The und asset of the options is SloppySoft Inc, that you estimate has a volatility of 83%, and expected to appreciate by more than 50% over the next 3 years. SloppySoft Inc’s closi at the NYSE today is $100. The firm pays no dividends. Assume the risk-free rate is a 0%. There is a fairly liquid set of call options on SloppySoft with a strike of K=97, and a 3 maturity. (a) How would you hedge your portfolio trading only the K=97 short-term option The delta of the portfolio is given by ∆ = 10(0.7639) + 5(0.7430) = 11.35 To make our portfolio delta neutral, given the K=97 options have a delta of 0.6106 need to trade x units of the K=97 such that ∆new = 11.35 + x(0.6106) = 0; x = −18.6; so we need to short 18.6 units of the K=9 (b) How would you hedge your portfolio trading if you could trade the K=97 short- options as well as SloppySoft Inc stock? The gamma of the options portfolio is Γ = 10(0.0021) + 5(0.0022) = 0.0326. We can make a delta/gamma-neutral portfolio by trading x units of the call and y of the stock such that ∆new = 11.35 + x(0.6106) + y = 0 Γnew = 0.0326 + x(0.0092) = 0 My calculations suggests we should short 3.53 units of the calls (x = −3.53) and sh 9.2 units of the underlying asset (y = −9.20).
No options (calls) 10.0 5.0 Delta/gamma- Asset price 100.0 100.0 100.0 Delta_POR Strike 100.0 110.0 97.0 Gamma_POR Time (years) 3.00 3.00 0.25 Risk-free return 0.00% 0.00% 0.00% Dividend yield 0.00% 0.00% 0.00% x Volatility 83.00% 83.00% 83.00% y 1+r_f 1.00 1.00 1.00 x 0.7188 0.6525 0.2809 N(x) 0.7639 0.7430 0.6106 N(x2) 0.2361 0.2162 0.4467 N'(x) 0.3081 0.3224 0.3835 Call price 52.7737 50.5144 17.7345 Delta_new Put price 52.7737 60.5144 14.7345 Gamma_new Delta call 0.7639 0.7430 0.6106 Delta put (0.2361) (0.2570) (0.3894) Gamma 0.0021 0.0022 0.0092
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
nnual risk-free rate is 10%. price K=35. on? d strike price K=35? annual risk-free rate is and strike price K=60. on? and strike price K=60?
The annual risk-free rate he stocks in two weeks? termining the constants u ce sigma is 44.66%, the
t is the (constant) risk- ortionally to its previous anges proportionally to its uropean Put option on ds before the expiration
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
y of the option anges proportionally to its uropean Put option on ng asset goes up we buy uidate our debt).
asset goes up we buy more t out). scount rate of 5%. The ke of K=40 and a one year ke of K=40 and a two year
1.05 0.0593 0.5236 0.3780 0.3982 the US. The SPZ is e of K=11 and a one year erms of investments in r maturity is trading for $3.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
g is fun! 11.3535 -18.5938 m call derlying d it is ing price a round orth f Slop- value suggest? utral.
11.35 0.00 m call derlying d it is ing price a round 3 month ns? 6, we 97 calls. -term units hort
-hedging is even more fun! 11.3535 0.0326 -3.53 units of calls K=97 -9.20 units of underlying 0.00 0.00
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
HW 3 - Q1a Price 100 Strike 110 pu 50.00% t 1 pd 50.00% RF 105% 120 u 1.20 90 d 0.90 4.76190476 10 p 3.83333333333 0 C0 18.6991869919 HW 3 - Q1b If the call option was trading for $3.20, can you generate an arbitrage profit Consider a binomial world in which a stock can go up in value by 20% or dow by 10% over the next year. The stock is currently trading at $100. The annual risk-f is 5%. Consider a call option that expires in one year and has a strike price of $ (a) (*) What should be the current value of the call option?
HW 3 - Q2a u 1.35 d 0.85 price 45 rf 105.00% Pu 0.4 0.42 stock payout Pd 0.6 0.58 45 60.75 2.19047619 strike 55 38.25 Payout 9.57142857 Consider a binomial world in which a stock can go up in value by 35% or down by 15% over the n currently trading at $45. The annual risk-free rate is 5%. (*) What is the risk-neutral probability that the stock will go up over the next y
HW 4 - Q1 Asset price 1,313.5 Strike 1,300.0 Time (years) 1.00 Risk-free retur 5.00% Dividend yield 2.00% Volatility 0.14619697933 1+r_f 1.05 x 0.3420 You know the current value of a call option on the S&P500 with a strike price of $1350 and one-ye S&P500 is currently trading for $1313.50, and it is expected to pay a 2% dividend yield over the nex term structure is flat at 5%. (a) What is the implied volatility of the call option? (b) Using the Black-Scholes model, what would you estimate the value of a put with of $1300 on the S&P500 to be?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
N(x) 0.6338 N(x2) 0.5776 N'(x) 0.3763 Call price 101.0586 Put price 51.4087 Delta call 0.6214 Delta put -0.3590 Gamma 0.0019 Theta call -54.1493 Theta put -19.2432 Vega 484.5465 HW 4 - Q2 Long Put Long call Quanitty 10 30 Asset price 100.0 100.0 100.0 Strike 90.0 100.0 110.0 Time (years) 1.00 1.00 1.00 Risk-free retur 5.00% 5.00% 5.00% Dividend yield 0.00% 0.00% 0.00% Volatility 25% 25% 25% 1+r_f 1.05 1.05 1.05 x 0.7416 0.3202 -0.0611 Consider the following prices of a set of European options with one-year matu Strike 90 100 110 Call price 18.07 12.28 7.98 Put price 3.78 7.51 12.74 You know the current value of the underlying asset is $100, and that the term struct at 5%. The above options are all priced as if the underlying asset had a 25% annual and all of the Black-Scholes assumptions held. Suppose you hold a long position in thirty call options with a strike of $100 and t options with a strike of $90. (a) How many call options with a strike of $90 would you need to trade in order to delta-neutral position? What would be the gamma of the combined position (b) How many call options with a strike of $90 and/or $110 would you need to trade to have a delta-neutral and gamma-neutral position?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
N(x) 0.7708 0.6256 0.4756 N(x2) 0.6885 0.5280 0.3779 N'(x) 0.3030 0.3790 0.3982 Call price 18.0693 12.2751 7.9784 Put price 3.7836 7.5132 12.7403 Delta call 0.7708 0.6256 0.4756 Delta put -0.2292 -0.3744 -0.5244 Gamma 0.0121 0.0152 0.0159 Theta call -6.6672 -7.1909 -6.9089 Theta put -2.4852 -2.5443 -1.7976 Vega 30.3029 37.9011 39.8199 number of calls delta port 16.4756614309 21.37375815034 Gamma 0.57602495667 Delta 0.000 Gamma 0.000 x 1.77528493163 y -37.515400605
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
t? wn free rate $110.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
5.75 0 0 16.75 next year. The stock is year?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
ear maturity is $76. The xt few years. The current h a strike
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
urity. ture is flat volatility, ten put o have a n? e in order
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Midterm Q1 Midterm Q2 Midterm Q3 Midterm Q3 The risk-neutral probability p that the stock goes up over the next period is always higher (i.e., more optimistic) than the true probability q. i. True ii. False It is never optimal to exercise an American call option early (i.e., before the expiration date) if the underlying asset is not expected to pay any dividends before the expiration date. i. True ii. False The ∆ of a call option i. is always larger than 1 ii. is always smaller than 1 iii. can be larger or smaller than 1 Consider a stock price with annual volatility sigma of 65% and an annual risk-free rate of 6%. What is the state price of the down state πd in a binomial model where the stock price changes proportionally to its previous value and each period corresponds to three weeks? i. 0.593 ii. 0.472 iii. 0.526
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Volatility 65% RF 6% t (weeks) 3 adjusted rf 1.003367 u 1.169 d 0.855 p 47.18% Pid 0.526 Midterm Q4 Price 177 Volatility 28% RF 7% t (months) 1 Strike 190 u 1.0841855258558 d 0.922351365289307 Su 191.900838076476 Sd 163.256191656207 Pu 0 Pd 26.7438083437926 rf adjust 1.00565414538741 p 0.514741633079828 P0 13 Midterm Q5 iii. 0.526 The current price of AAPL is $177 and its annual volatility is 28%. The annual risk-free rate is 7%. If the AAPL price can only go up or down over the next month, what is the current price of an American put option with strike price $190 that expires in one month? Gold is trading for $100. Assume that it is expected to appreciate by 20% over the next year. You also know that the volatility of gold’s returns is 25%, and that the risk-free rate is 10%.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Asset price 100.0 Strike 100.0 Time (years) 1.00 Risk-free return 10.00% Dividend yield 0.00% Volatility 25.00% 1+r_f 1.10 x 0.5062 N(x) 0.6937 N(x2) 0.6011 N'(x) 0.3510 Call price 14.7186 Put price 5.6277 Short (0.3063) Delta call 0.6937 Lend 36.26 Delta put (0.3063) Gamma 0.0140 Theta call (9.5954) Theta put (0.9309) Vega 35.0962 Midterm Q6 You also know that the volatility of gold’s returns is 25%, and that the risk-free rate is 10%. (a) The price of a put option with a strike of K = 100 on gold with a one year maturity, according to the Black-Scholes model, is $5.63. (b) One should short 0.3063 units of gold, and lend $36.26. (c) The ∆ of the firm’s portfolio is −0.3063, so taking a long position in gold of 0.3063 units would make the portfolio ∆-neutral. Fifty-cents, a violist-turned-rapper, is desperately trying to purchase som stock. He would like to essentially eliminate the downside risk of his portf is long Eminem. Unfortunately, options are not traded on Eminem, so achieve the downside protection Fifty-cents is yearn You have been hired to offer Fifty-cents some advice as to what investm order to get him some downside protection. Fifty-cents argues that he do money in order to guarantee himself that his stock holdings do not drop would like to be able to sell his shares for at least $40 in thre The current price of Eminem is $50, and you know that this stock will 40% over each of the following months (with equal real probabilities q Eminem’s stock price over the next three months is thereby given by th
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Stock Tree RF 101% 50 70 t (months) 3 30 Strike 40 u 1.4 d 0.6 Pu 0.5125 Put price tree Pd 0.4875 8.53236548 3.44800755 14.0524826 Delta Cash -0.265111876286639 -0.127563649222065 0 21.7879593 -0.602516501650165 -0.44047619047619 -1 Eminem’s stock price over the next three months is thereby given by th 50 70 98 137.2 30 42 58.8 18 25.2 10.8 There is a riskless asset that pays a riskless return of 1% each month, an 1% over the next three months. 1. Assess what you would consider to be a fair price for a three-mont with a strike of $40. 8.53 2. How can Fifty-cents achieve the downside protection he is looking f on the Eminem stock and cash? Be explicit about the amount of sha hold at each point in time, as a function on the evolution of Note: I would like you to tell Fifty-cents how much stock and bonds different states, and at t = 2 in three different states. Clearly, you sho position. 3. After further consideration, Fifty-cents is wondering how much mor a bit more protection, in particular getting at least $45 instead of $4 months. Assess the extra cost of this higher protection on Fifty-cent dynamic trading strategy would you recommend in order to achieve Note: I would like you to tell Fifty-cents how much stock and bonds different states, and at t = 2 in three different states. Clearly, you sho position.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Price 50 stock RF 101% 50 70 t (months) 3 30 Strike 45 u 1.4 d 0.6 Pu 0.5125 Put price Pd 0.4875 10.867867 4.61287496 17.6665584 Delta Cash -0.326342086560141 -0.170659476661952 0 27.1849713 -0.708230198019802 -0.58928571428572 -1 Midterm Q7 Trader Smurf has just finished a very busy day. After much trading in the day with the following inventory of options on mushrooms: a long po a strike of K = 100 and 6-month maturity, a short position in 80,000 p K = 90 and 3-month maturity, and a long position in 50,000 puts wit 6-month maturity. Trader Smurf also has about $500,000 in cash after a the risk-free rate of interest (5%). Mushrooms, a very liquid commodity in the world of Smurfs, are curr volatility of monthly returns from investing in mushrooms over the rec 1. Estimate the value of Trader Smurf’s portfolio using Bla 2. How can Trader Smurf hedge his position by trading on the underly 3. If Trader Smurf could trade both on the underlying asset (mushroom options that he owns (those with K = 95), what trading strategy wou order to be hedged against movements on the underly 4. If Trader Smurf could trade both on the underlying asset (mushroom options that he owns (those with K = 95), what trading strategy wou order to be hedged against movements on the underlying asset and m mushroom returns? © Buffa-Garc ıa, Leeds School of Business Page 4 ́
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Long position Calls Short position puts Long position puts Quanitity 100 80 50 Stike 100 90 95 T Months 6 3 6 Asset price 96.0 Asset price 96.0 Strike 100.0 Strike 90.0 Time (years) 0.50 Time (years) 0.25 Risk-free return 5.00% Risk-free retur 5.00% Dividend yield 0.00% Dividend yield 0.00% Volatility 0.29999119987093 Volatility 0.2999912 1+r_f 1.05 1+r_f 1.05 x 0.0286 x 0.5866 N(x) 0.5114 N(x) 0.7213 N(x2) 0.4272 N(x2) 0.6688 N'(x) 0.3988 N'(x) 0.3359 Call price 7.4054 Call price 9.7790 Put price 8.9955 Put price 2.6879 Delta call 0.5114 Delta call 0.7213 Delta put -0.4886 Delta put -0.2787 Gamma 0.0196 Gamma 0.0233 Theta call -10.1549 Theta call -12.5744 Theta put -5.3934 Theta put -8.2365 Vega 27.0700 Vega 16.1226 Price of portfolio 847.13 How to hedge 53.77 short Gamma of portfolio 1.04 Delta 0.000 Gamma 0.000 x -75.3605421283718 short y -54.8791535093162 Vega of portfolio 2,722.63 Delta (0.00) Vega (0.00)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
x -94.7958541337099 short y -104.280580995587 need to sell current holdings of 50 and short 54
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
vol 65% Rf 6% t (weeks) 3.00 adjusted rf 1.00336732 u 1.16897226
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
d 0.85545229 p 0.47178824 pid 0.52643907 PUT price 177 vol 28% rf 7% Strike 190 t (months) 1 u 1.08418553 d 0.92235137 Su 191.900838 sd 163.256192 Pu 0 Pd 26.7438083 rf adjust 1.00565415 p 0.51474163 P0 13
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
me put options on Eminem tfolio, which at the moment o it is not that simple to ning for. ment strategy to follow in oes not mind spending some p in value below $40, i.e. he ee months time. go up by 40% or down by q = 0.5). The evolution of he following binomial tree:
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
98 137.2 42 58.8 18 25.2 10.8 payofff 0 0 7.14356436 0 21.6039604 14.8 29.2 12.377463 0 32.1279776 25.6435644 39.6039604
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
98 137.2 42 58.8 18 25.2 10.8 payoff 0 0 9.55693069 0 26.5544554 19.8 34.2 16.5590383 0 38.9134644 34.3069307 44.5544554 the CBOE, he has closed osition in 100,000 calls with puts with a strike price of th a strike of K = 95 and all this hard work, earning rently trading at $96. The cent past has been 8.66%. ack-Scholes. ying asset (mushrooms)? ms) and the at-the-money uld you recommend in ying asset? ms) and the at-the-money uld you recommend in movements in volatility of 4 of 4
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Cash 500000 RF 5% Current price 96 Vol 8.66% 0.2999912 Asset price 96.0 Strike 95.0 Time (years) 0.50 Risk-free retur 5.00% Dividend yield 0.00% Volatility 0.2999912 1+r_f 1.05 x 0.2704 N(x) 0.6066 N(x2) 0.5232 N'(x) 0.3846 Call price 9.7217 Put price 6.4322 Delta call 0.6066 Delta put -0.3934 Gamma 0.0189 Theta call -10.1992 Theta put -5.6759 Vega 26.1087
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
4.2
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help