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.
This is a part of the course
“Quantitative Risk Management in R”
Exercise instructions
- Set the current interest rate
rto be 0.01, the current volatilitysigmato be 0.2 and the strikeKto be 100. - Look at the arguments of the
Black_Scholes()function. - Price a European call option that matures in
T = 1year if the current stock price isS = 80. - Price a European call option that matures in
T = 1year if the current stock price isS = 120. - Price a European put option that matures in
T = 1year if the current stock price isS = 80. - Price a European put option that matures in
T = 1year if the current stock price isS = 120.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Set the interest rate r to be 0.01, the volatility sigma to be 0.2 and the strike K to be 100
r <- 0.01
# Look at the arguments of the Black_Scholes function
args(___)
# Price a European call option that matures in one year if the current stock price is 80
Black_Scholes(0, ___, r, sigma, K, 1, "call")
# Price a European call option that matures in one year if the current stock price is 120
# Price a European put option that matures in one year if the current stock price is 80
Black_Scholes(___, ___, r, sigma, K, ___,"put")
# Price a European put option that matures in one year if the current stock price is 120