Calculate the Price of a Put Option with the Same Exercise Price

What is the price of a put option with the same exercise price as a call option that is selling for $3.45 and expires in three months, given that the current stock price is $38 per share and the exercise price is $45 with a risk-free rate of interest of 4.47% per year compounded continuously?

The price of a put option with the same exercise price is $5.47.

Understanding Black-Scholes Formula for Put Options

To calculate the price of a put option with the same exercise price as the call option provided, we can utilize the Black-Scholes formula. This formula is commonly used in options trading to determine the theoretical price of European-style options. Key Components of the Black-Scholes Formula: 1. Put Option Price = Exercise Price * e^(-r * t) * N(-d2) - Stock Price * N(-d1) 2. Exercise Price: The price at which the option can be exercised 3. e: The base of the natural logarithm (approximately 2.71828) 4. r: Risk-free interest rate per year, compounded continuously 5. t: Time to expiration in years 6. N(): Cumulative standard normal distribution function 7. d1 and d2: Calculated parameters based on market variables

Calculating the Put Option Price:

First, we need to compute the values of d1 and d2 using the given information and the Black-Scholes formula. Subsequently, we can substitute these values, along with the Stock Price, Exercise Price, Time to Expiration, and Risk-Free Interest Rate, into the formula to determine the price of the put option. Detailed Steps: 1. Determine the values of d1 and d2 using the provided formulas. 2. Input the calculated values and other variables into the Black-Scholes formula. 3. Solve for the price of the put option with the same exercise price as the call option. By following these steps and utilizing the Black-Scholes formula, we arrive at the final answer of $5.47 as the price of a put option with the same exercise price. This calculation enables investors to make informed decisions regarding options trading strategies and financial risk management.
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