Investments
11th Edition
ISBN: 9781259277177
Author: Zvi Bodie Professor, Alex Kane, Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 21, Problem 33PS
Summary Introduction
To calculate: European put option for 1 year using binomial model with exercise price $110 and also confirms that put price satisfies put- call parity or not.
Introduction: The put call parity equation is used to find values of put and call option. Here we verify the put value using binomial model and parity equation.
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Students have asked these similar questions
Assume that the two-period Binomial
Option Pricing model holds (n=2),
with the following information (t = 1
year, S = $40, u = 1.1, d =0.9, K= $45,
and r = 10%). What is the value of this
* ?European call option
%3D
%3D
Q2: Given the following inputs for YMMV:
Interest rate
3.25
Dividend rate
3.00
Spot Price
Volatility (%)
30.21
12.00
Strike Price
30.00
Expiry (months) T
Option type
12
European Put
a) Compute u, d, Pup; Pdn, Construct a 3 step tree and price the option.
Use the following data to estimate the value of a European put option with X = $120. The current stock price now is SO = $100. The two possibilities for ST are $150 and $80. If the risk-free rate is 10%, estimate the value of the put option now.
a. P0 = $0 b. P0 = $40 c. P0 = $20.78 d. P0 = $22.86
Chapter 21 Solutions
Investments
Ch. 21 - Prob. 1PSCh. 21 - Prob. 2PSCh. 21 - Prob. 3PSCh. 21 - Prob. 4PSCh. 21 - Prob. 5PSCh. 21 - Prob. 6PSCh. 21 - Prob. 7PSCh. 21 - Prob. 8PSCh. 21 - Prob. 9PSCh. 21 - Prob. 10PS
Ch. 21 - Prob. 11PSCh. 21 - Prob. 12PSCh. 21 - Prob. 13PSCh. 21 - Prob. 14PSCh. 21 - Prob. 15PSCh. 21 - Prob. 16PSCh. 21 - Prob. 17PSCh. 21 - Prob. 18PSCh. 21 - Prob. 19PSCh. 21 - Prob. 20PSCh. 21 - Prob. 21PSCh. 21 - Prob. 22PSCh. 21 - Prob. 23PSCh. 21 - Prob. 24PSCh. 21 - Prob. 25PSCh. 21 - Prob. 26PSCh. 21 - Prob. 27PSCh. 21 - Prob. 28PSCh. 21 - Prob. 29PSCh. 21 - Prob. 30PSCh. 21 - Prob. 31PSCh. 21 - Prob. 32PSCh. 21 - Prob. 33PSCh. 21 - Prob. 34PSCh. 21 - Prob. 35PSCh. 21 - Prob. 36PSCh. 21 - Prob. 37PSCh. 21 - Prob. 38PSCh. 21 - Prob. 39PSCh. 21 - Prob. 40PSCh. 21 - Prob. 41PSCh. 21 - Prob. 42PSCh. 21 - Prob. 43PSCh. 21 - Prob. 44PSCh. 21 - Prob. 45PSCh. 21 - Prob. 46PSCh. 21 - Prob. 47PSCh. 21 - Prob. 48PSCh. 21 - Prob. 49PSCh. 21 - Prob. 50PSCh. 21 - Prob. 51PSCh. 21 - Prob. 52PSCh. 21 - Prob. 53PSCh. 21 - Prob. 1CPCh. 21 - Prob. 2CPCh. 21 - Prob. 3CPCh. 21 - Prob. 4CPCh. 21 - Prob. 5CP
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- Please explain both a and b Thanksarrow_forwardWhat is the gamma of a European call option with the following parameters? As a reminder, gamma is defined as the first derivative of delta with respect to the stock price, or alternatively as the second derivative of the option price with respect to the stock price. s0 = $40k = $40 r = 10%sigma = 20%T = 0.75 years In order to avoid precision issues with Excel, please use an epsilon of 0.0001. (required precision 0.0001 +/- 0.0002) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂rarrow_forwardGiven the following information, predict the European call option's new price after the risk free rate changes. Initial call option price = $3 Initial risk free rate = 9.9% Rho = 9 New risk free rate = 9.5% (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r Recall that rho is defined as the partial derivative of the option's price with respect to the risk free rate. (i.e. rho = ∂π / ∂r).arrow_forward
- Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?arrow_forwardLet S = $85, r = 4% (continuously compounded), d = 3%, s = 35%, T = 1.5. In this situation, the appropriate values of u and d are 1.36426 and 0.74408, respectively. Using a 2-step binomial tree, calculate the value of a $80-strike European call option.arrow_forwardWhat is the rho of a European put option with the following parameters? As a reminder, rho is defined as the first derivative of the option price with respect to the risk free rate. s0 = $40k = $39 r = 10%sigma = 20%T = 0.75 years (required precision 0.01 +/- 0.01) Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂rarrow_forward
- 2. These options are traded in the market: call option with an Exercise (Strike) Price of 1.15 $/€ and premium (option cost) of 0.03 $ per euro. (a) If the Spot exchange rate is 1.17 $/ €, is the option ITM, ATM or OTM? (b) Calculate Intrinsec value and Time value of the option. (c) If put options are traded with same Exercise Price at same cost of 0.03 $ per euro and Fwd for the same maturity is traded at 1.17 $/ €, how can an astute tradem arbitrage? Explain. (d) Calculate Intrinsec value and Time value of the put option mentioned above.arrow_forwardWrite down the formula for: fa) price of an European put option f6) price of a European calli option Koth on a non-dividend paying stock and Koth derived from the Black-Scholes-Merton Differential Equations Define every symbol in the formulae. Given that, with the usual notation, S, = 42, K = 40, r3D0.1, о %3D0.2, Т%3D0.5 N(0.7693) N(0.6298) = 0.7340 0.7791 4.79 Calculate the price of a European call option on the stock. Consider an option on a dividend paying stock with the following characteristics s, = $30 Going ex-dividend in 1.5 months. Expected Dividend is $0.5 Exercise Price is $29. Risk free rate is 5% per annum Volatility is 25% per annum Time to maturity is 4 months Calculate price if (a) European Call (b) European Put 2.52 2.52 Given further N (.3068) = 0.6205 N (.1625) = 0.5645arrow_forwardSuppose you want to price an American style put option for a stock being traded on theKuispad Stock Exchange having the following parameters: s = 18, t = 0.25, K = 20, σ = 0.2, r = 0.07. Using n = 5, calculate the value of V0(0). Provide all necessary detailsarrow_forward
- 2. (Pricing Call Options) Consider a l-period binomial model with R = 1.05, So = 50, u = 1/d = 1.08. What is the value of a European call option on the stock with strike K = 52, assuming that the stock does not pay dividends? Please submit your answer rounded to two decimal places. So for example, if your answer is 5.489 then you should submit an answer of 5.48 or 5.49.arrow_forwardLet S = $50, r = 4% (continuously compounded), d = 1%, s = 40%, T = 1.5. In this situation, the appropriate values of u and d are 1.44616 and 0.72332, respectively. Using a 2-step binomial tree, calculate the value of a $55-strike European put option. a. $9.203 b. $11.323 c. $11.205 d. $10.874 e. $10.552arrow_forwardMf2. Assume a one-period binomial model in which the initial stock price is S = 60 and in each period the stock price can go either up by a factor of u = 7 3 or down by a factor of d = 2 3 . Assume that the simple interest rate over one time period is r = 1 3 . (a) Determine the fair price of the European put option with strike K = 60. (b) Assume that instead of the price determined in part (a), the European call option is trading at 11. Prove that there is an arbitrage and explain how the arbitrage can be achievedarrow_forward
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