Homework Answers
The correct answer is the last option i.e. option e. $ 2.47
Black Scholes formula for dividend paying stock with dividend yield q will be:
Let'splug in the values to get:
The correct answer is the last option i.e. option e. $ 2.47
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Let S - $78,0 - 40%,r-6,5%, and 8 - 2% (continuously compounded). Compute the Black-Scholes price...
Let S - $53, -27%,r-5.5%, and 8-2% (continuously compounded). Compute the Black-Scholes delta (A) of a...
Let S - $53, -27%,r-5.5%, and 8-2% (continuously compounded). Compute the Black-Scholes delta (A) of a $55-strike European call option with 6 months until expiration O a.-0.5619 Ob -0.4977 OC 0.4923 Od-0.6132 O 0.0.4411
Let S - $57,0 -29%,r-7.5%, and 8 - 2.5% (continuously compounded). Compute the Black-Scholes vega of...
Let S - $57,0 -29%,r-7.5%, and 8 - 2.5% (continuously compounded). Compute the Black-Scholes vega of a $55-strike European call option with 3 months until expiration. (That is, compute the approximate change in the call price given a 1 percentage point increase in O.) O a. 0.1276 O b.0.1092 OC 0.1175 O d. 0.1862 0.0.1041
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a...
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). You want to protect your long position against losses and decide to buy a European put option on AAPL with a strike price of $180.15 and an expiration date of 1-year from today. The continuously compounded risk free interest rate is 8% and the stock pays no dividends. The current stock price for AAPL is $200 and its...
1a) The current price of a stock is $43, and the continuously compounded risk-free rate is...
1a) The current price of a stock is $43, and the continuously compounded risk-free rate is 7.5%. The stock pays a continuous dividend yield of 1%. A European call option with a exercise price of $35 and 9 months until expiration has a current value of $11.08. What is the value of a European put option written on the stock with the same exercise price and expiration date as the call? Answers: a. $5.17 b. $3.08 c. $1.49 d. $2.50...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on the equity in Amgen, which has the following characteristics. Expiration: Current stock price of Amgen: Strike Price: Volatility of Amgen Stock price: Risk-free rate (continuously compounded): Dividends: 3 months (i.e., 60 trade days) $53.00 $50.00 26% per year 2% None If the market price of the Amgen put is actually $2.00 per share, is the above estimate of volatility higher or lower than the...
In this question we assume the Black-Scholes model. We denote interest rate by r, drift rate...
In this question we assume the Black-Scholes model. We denote interest rate by r, drift rate pi and volatility by o. A European power put option is an option with the payoff function below, Ka – rº, ha if x <K, 0, if x > K, for some a > 0. In particular, it will be a standard European put option when a = 1. (a) Derive the pricing formula for the time t, 0 <t< T, price of a...
Thanks anyway! For a stock, you are given: •The stock’s price is 40. •The continuously compounded...
Thanks anyway! For a stock, you are given: •The stock’s price is 40. •The continuously compounded risk-free interest rate is 5%. •The stock’s continuous dividend rate is 2%. •A one-year 35-strike European call option has premium of 10. •A one-year 45-strike European call option has premium of 2. Determine the lowest and highest arbitrage-free premiums for a one-year 40-strike European put option on the stock.
14. Note that the Black-Scholes formula gives the price of European call c given the time...
14. Note that the Black-Scholes formula gives the price of European call c given the time to expiration T, the strike price K, the stock’s spot price S0, the stock’s volatility σ, and the risk-free rate of return r : c = c(T, K, S0, σ, r). All the variables but one are “observable,” because an investor can quickly observe T, K, S0, r. The stock volatility, however, is not observable. Rather it relies on the choice of models the...
14. The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free...
14. The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You are given that the price of a 35-strike call option is 3.35 higher than the price of a 40-strike call option, where both options expire in 3 months. Calculate the amount by which the price of an otherwise equivalent 40-strike put option exceeds the price of an otherwise equivalent 35-strike put option. (A) B) 1.55 1.65 1.75 3.25 3.35
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months...
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months European put option with strike K 8 EUR is 2 EUR Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6...
Let S - $53, -27%,r-5.5%, and 8-2% (continuously compounded). Compute the Black-Scholes delta (A) of a $55-strike European call option with 6 months until expiration O a.-0.5619 Ob -0.4977 OC 0.4923 Od-0.6132 O 0.0.4411
Let S - $57,0 -29%,r-7.5%, and 8 - 2.5% (continuously compounded). Compute the Black-Scholes vega of a $55-strike European call option with 3 months until expiration. (That is, compute the approximate change in the call price given a 1 percentage point increase in O.) O a. 0.1276 O b.0.1092 OC 0.1175 O d. 0.1862 0.0.1041
Assume the Black-Scholes framework for options pricing. You are a portfolio manager and already have a long position in Apple (ticker: AAPL). You want to protect your long position against losses and decide to buy a European put option on AAPL with a strike price of $180.15 and an expiration date of 1-year from today. The continuously compounded risk free interest rate is 8% and the stock pays no dividends. The current stock price for AAPL is $200 and its...
Problem 1: - Using the Black/Scholes formula and put/call parity, value a European put option on the equity in Amgen, which has the following characteristics. Expiration: Current stock price of Amgen: Strike Price: Volatility of Amgen Stock price: Risk-free rate (continuously compounded): Dividends: 3 months (i.e., 60 trade days) $53.00 $50.00 26% per year 2% None If the market price of the Amgen put is actually $2.00 per share, is the above estimate of volatility higher or lower than the...
In this question we assume the Black-Scholes model. We denote interest rate by r, drift rate pi and volatility by o. A European power put option is an option with the payoff function below, Ka – rº, ha if x <K, 0, if x > K, for some a > 0. In particular, it will be a standard European put option when a = 1. (a) Derive the pricing formula for the time t, 0 <t< T, price of a...
14. The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest rate is 8%. You are given that the price of a 35-strike call option is 3.35 higher than the price of a 40-strike call option, where both options expire in 3 months. Calculate the amount by which the price of an otherwise equivalent 40-strike put option exceeds the price of an otherwise equivalent 35-strike put option. (A) B) 1.55 1.65 1.75 3.25 3.35
Question 3 (30 Points) (a) Assume that So 10 EUR and r price of a 9-months European put option with strike K 8 EUR is 2 EUR Compute the price of a 9-months European call option with same strike and same underlying. Which relation did you use? (b) A 6-month European call option on a non-dividend-paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6...
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