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Exercise

Compute Black-Scholes price of an option

The Black_Scholes() function in the package qrmtools can be used to price European call and put options using the standard Black-Scholes options pricing formula for a non-dividend-paying stock.

In this exercise you will price in succession: an out-of-the-money European call, an in-the-money European call, an in-the-money European put and an out-of-the-money European put. An option is in-the-money if immediate exercise would result in a positive payout and out-of-the-money if it would not.

The main point of the exercise is to understand the different risk factors that go into the price calculation: the current stock price, the current volatility and the current interest rate.

Instructions

100 XP
  • Set the current interest rate r to be 0.01, the current volatility sigma to be 0.2 and the strike K to be 100.
  • Look at the arguments of the Black_Scholes() function.
  • Price a European call option that matures in T = 1 year if the current stock price is S = 80.
  • Price a European call option that matures in T = 1 year if the current stock price is S = 120.
  • Price a European put option that matures in T = 1 year if the current stock price is S = 80.
  • Price a European put option that matures in T = 1 year if the current stock price is S = 120.