The following market information will be used for this problem.TodaySpot (S/unit)Volatilityrisk-free interest rateDividend yleldMay 1, 20219818.00%2.00%0.00%You sell 8,000 European call options with a strike of 93 and maturity July 6, 2022 at fair value.Option information for a variety of stock prices are:Spot Price Option Price Option Delta % Option Delta Shares64.8344X66,7796X6৪.6613४70.4772%172.2256%10.15166910.80979111.48704996-5,187-5,3425,493-5,638-5,77897989910012.18279712.896368Note, the current stock price is in the middle of the table.To hedge your position, how many shares do you buy or sell? Assume you can only trade a whole number ofshares.The market moves to 96. You re-balance your delta hedge by buying or selling how many shares?The market moves back to 98. You re-balance your delta hedge by buying or selling how many shares?How much money have you made or lost on your overall position?

Delta hedging is the strategy of options trading used to cover the risk of change in the price of…

Answered: The following market information will…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose the following for European options: Stock price $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading ot $5 and there is an identical call option that is trading for $4. The arbitrage gain that can be made is equal to: O a. $2.00 b. $0.27 Oc. $3.00 O d. $1.27 O e $227
M6
Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option X
Dd11.
Required: Refer to Figure 15.1, which lists the prices of various Microsoft options. Use the data in the figure to calculate the payoff and the profit/loss for investments in each of the following December 2019 expiration options on a single share, assuming that the stock price on the expiration date is $137. (Loss amounts should be indicated by a minus sign. Round "Profit/Loss" to 2 decimal places.) a. Call option, X = 135 b. Put option, X = 135 es c. Call option, X = 145 d. Put option, X = 145 Payoff Profit/Loss
Calculate the price of a call and a put option based on the Black-Scholes option pricing.
What 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/∂r
ANSWER C AND D PLEASE ONLY In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.a) Find prices of Arrow-Debreu securities.b) Calculate the price of a call option by constructing and pricing areplicating portfolio. c) Calculate the price of a put option by RNVR.d) Does put-call parity hold? Explain.
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.
3. Consider a European call option on a non-dividend paying stock with exercise price 100 USD and expiration in one month. Interest rate is 1 percent and volatility of the stock is 0.4. Stock price 90 USD. Option price?? Use excel.
(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
F3

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