Question

A stock price is currently $40. It is known that at the end of one month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. Use put-call parity to solve the value of the corresponding put option.

Answer 1

Call option details not given.

Yet assuming strike price, X=$40 with call option expiring in month.

Value of call option by binomial option pricing model is calculated as follows.

Probability of up move,

where u and d are up and down move values in percentage terms,u=(Su/S)=(42/40)=1.05, d=(Sd/S)=(38/40)=0.95.

So, p=0.567

Solving this,

Upstate payoff=max(Su-X,0)=max($42-$40,0)=$2. Downstate payoff=max(Sd-X,0)=max($38-$40,0)=$0.

Expected payoff = (0.567*2)+(0.433*0) = $1.134 (Multiplying probabilities with payoffs in each state)

Now, discounting this to get present value of expected payoff

Value of call option=$1.1265.

Using put call parity for put option,

put option value, .

Remember, since question does not mention strike price of call option, X=$40 is used. If any other strike price is mentioned, just replace $40 with given value wherever X is used in equation.