Final answer:
To calculate the price of the call option, we use the put-call parity relationship with the given values: current stock price at $53, put option price at $6.1, strike price at $50, and the risk-free interest rate at 3%, assuming a two-month expiration.
Step-by-step explanation:
Black-Scholes Option Pricing Model
The subject in question refers to the valuation of financial derivatives, specifically, the calculation of a call option price given the price of a put option. This is typically approached using the Black-Scholes model. According to the put-call parity, a put and a call option with the same strike price and expiration date, on the same underlying stock, should have a predictable relationship in pricing. To calculate the call option price given the current stock price of $53, the put option price of $6.1, strike price of $50, and the risk-free rate of 3%, we use the put-call parity formula:
C + X/(1+r)^n = P + S
where
- C is the call option price,
- X is the strike price,
- r is the risk-free interest rate,
- n is the time to expiration,
- P is the put option price,
- S is the current stock price.
Assuming the time to expiration is two months, we can substitute the known values into the equation to find the unknown call option price.