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`

.