Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. A. Using the Black model, calculate the price of a call option on a forward contract. B. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset. Should this pricing be any different from the one calculated in letter A? Explain your answer. C. Using the Black model, calculate the price of a put option on a forward contract. D. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset. Should this pricing be any different from the one calculated in letter C? Explain your answer.

Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. A. Using the Black model, calculate the price of a call option on a forward contract. B. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset. Should this pricing be any different from the one calculated in letter A? Explain your answer. C. Using the Black model, calculate the price of a put option on a forward contract. D. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset. Should this pricing be any different from the one calculated in letter C? Explain your answer.

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter11: Managing Transaction Exposure

Section: Chapter Questions

Problem 56QA

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Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black model, calculate the price of a call option on a forward contract.
Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black model, calculate the price of a put option on a forward contract.
You are considering a European put option and a European call option on ABC Ltd and have available the following information. The put option with an exercise price of $15 and time to maturity of 60 days is priced at $2.00. The call option with the same exercise price and time to maturity is priced at $3.00. The underlying asset price is $15. The risk-free rate is 2% per 60 days. Could an arbitrage profit be earned? If so, how much the arbitrage profit is? Show your works (Hint: use discrete put-call parity equation and consider two scenarios for stock price at maturity of the options: $10 or $20).
What would be your dollar return had you purchased a single contract at the call premium when the SPY price was $464.72 and sold at the expected call premium if the underlying SPY price increased to $490 (do not round the forecasted premium)? Strike = 485, Last price = 4.64, Bid = 4.67, Ask = 4.72. The current price for SPY is $464.72. The implied volatility for this option is 11.23% per annum. The risk-free rate is 1% per annum.
Consider an American put option with time to expiry 15 months, and a strike of 74. The current price of the underlying is 71. Divide the time to expiry into three 5-months intervals. Assume that in each 5-months interval, the price can either rise by 5, or fall by 5, with unknown probability. The risk-free (continuously compounding) rate is 0.042. Using a binomial tree, identify the circumstances under which early exercise would be rational for the holder of this option. Draw the binomial tree and show the necessary calculation and briefly explain the answer.
Consider a European Call Option with a strike of 82. The current price of the underlying asset is 80, and the time to expiry is 5 months. The current market price of the option is 6.22. The risk-free rate is 4.1%. (b) You believe the true volatility is 28.4%. Is the option under-priced or overpriced? Hence what position should you take in option to make money. Explain. (Please provide Screenshots.)
Suppose a European call option on a sack of corn with a strike price of $50 and a maturity of one-month, trades for $5. What is the price of the put premium with identical strike price and time until expiration, if the one-month risk-free rate is 2% and the spot price of the underlying asset is $53?
Suppose that the current spot price of corn is $720 per bushel. The one year risk-free rate is 6% per annum. The futures price for delivery of one bushel of corn in one year’s time is $792 per bushel. Assume that net costs (storage costs minus convenience yield) are $15 per bushel (over the next one year). Is the futures contract correctly priced? If not, what is the theoretically correct price for the futures contract and how could you take advantage of any mispricing? Please show full steps and explain.
Consider a one-period binomial model in which the underlying is at 65 Euros, and can go up 30% or down 22% each period. The risk-free rate is 8%. European Put Option with Execution Price of 70 Euros. Assume that the put is selling for 9 Euros. Demonstrate how to execute an arbitrage transaction and calculate the rate of return. Use 10000 puts.
A one-year gold futures contract is selling for $1,247. Spot gold prices are $1,200 and the one-year risk-free rate is 2%. a) According to spot-futures parity, what should be the futures price? b) What risk-free strategy can investors use to take advantage of the futures mispricing, and what would be the profits from that strategy?