Consider a non-dividend-paying stock with a current price of $50. A 6-month forward contract on the stock is available for purchase. The risk-free interest rate is 4% per annum, compounded continuously. An investor believes that in 6 months, the stock price will either increase by 20% or decrease by 10%. The investor also believes that there is a 60% probability of the stock price increasing and a 40% probability of the stock price decreasing. The investor is considering two strategies: 1. Strategy A: Buy the stock today and hold it for 6 months. 2. Strategy B: Buy the 6-month forward contract on the stock. Part 1: Calculate the forward price of the stock. Part 2: Calculate the expected stock price in 6 months and the expected payoff for each strategy. Part 3: Calculate the minimum amount the investor would be willing to pay for an option that would allow them to buy the stock in 6 months at the forward price.

Consider a non-dividend-paying stock with a current price of $50. A 6-month forward contract on the stock is available for purchase. The risk-free interest rate is 4% per annum, compounded continuously. An investor believes that in 6 months, the stock price will either increase by 20% or decrease by 10%. The investor also believes that there is a 60% probability of the stock price increasing and a 40% probability of the stock price decreasing. The investor is considering two strategies: 1. Strategy A: Buy the stock today and hold it for 6 months. 2. Strategy B: Buy the 6-month forward contract on the stock. Part 1: Calculate the forward price of the stock. Part 2: Calculate the expected stock price in 6 months and the expected payoff for each strategy. Part 3: Calculate the minimum amount the investor would be willing to pay for an option that would allow them to buy the stock in 6 months at the forward price.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter20: Financing With Derivatives

Section20.A: The Black-scholes Option Pricing Model

Problem 1P

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Consider a non-dividend-paying stock with a current price of $50. A 6-monthforward contract on the stock is available for purchase. The risk-free interest rate is 4% perannum, compounded continuously.An investor believes that in 6 months, the stock price will either increase by 20% or decreaseby 10%. The investor also believes that there is a 60% probability of the stock price increasingand a 40% probability of the stock price decreasing.The investor is considering two strategies:1. Strategy A: Buy the stock today and hold it for 6 months.2. Strategy B: Buy the 6-month forward contract on the stock.Part 1: Calculate the forward price of the stock. (i think this = 50*e^(.04*.5)=50e^.02=51.01)Part 2: Calculate the expected stock price in 6 months and the expected payoff for each strategy.Part 3: Calculate the minimum amount the investor would be willing to pay for an option thatwould allow them to buy the stock in 6 months at the forward price.
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