Question

Use DerivaGem to calculate the value of an American put option on a non-dividend-paying stock when the stock price is USD 30, the strike price is USD 32, the risk-free rate is 5% p.a. continuously compounded, the volatility is 30% p.a. and the time to maturity is 1.5 years. (Choose ‘Binomial American’ for the option type and 50 time steps.) (See textbook Chapter 13 for supporting theory and materials)

1. Calculate the option’s intrinsic value. Calculate the option’s time value.
2. What would a time value of zero indicate? What is the value of an option with zero time value?
3. Using a trial and error approach, calculate how low the stock price would have to be for the time value of the option to be zero. (use 50 time steps)

Answer 1

a) Intrinsic value of a Put Option = Strike price – Current price

Intrinsic value = $32 - $30 = $2

Time value of an option = Option Premium - Intrinsic Value

Time value = $5.5241 - $2 = $3.5241 or $3.52 (Rounded-off to two decimal)

Note: The option premium is calculated using DerivaGem software as directed in the question. Below is the image, how it was calculated.

b) A time value of zero would indicate that the “intrinsic value” and the “option premium” are equal.

c) Using trial and error in the calculator, it was found that the current stock price needs to be $27.16 for the time value of the option to be zero. At this price level, the option premium is $4.84 (rounded-off figure) and the intrinsic value is -$4.84 resulting in a zero time-value.