Use DerivaGem to calculate the value of an American put...

Use DerivaGem to calculate the value of an American put option on a non-dividend. paying stock when the stock price is $\$ 30,$ the strike price is $\$ 32,$ the risk-free rate is $5 \%,$ the volatility is $30 \%$, and the time to maturity is 1.5 years. (Choose "Binomial American" for the "option type" and 50 time steps.) (a) What is the option's intrinsic value? (b) What is the option's time value? (c) What would a time value of zero indicate? What is the value of an option with zero time value? (d) 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 DerivaGem to calculate the value of an American put option on a non-dividend. paying stock when the stock price is $\$ 30,$ the strike price is $\$ 32,$ the risk-free rate is $5 \%,$ the volatility is $30 \%$, and the time to maturity is 1.5 years. (Choose "Binomial American" for the "option type" and 50 time steps.)
(a) What is the option's intrinsic value?
(b) What is the option's time value?
(c) What would a time value of zero indicate? What is the value of an option with zero time value?
(d) 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.

Key Concepts

Intrinsic Value

Intrinsic value refers to the immediate exercise value of an option if it were exercised right now. For a put option, it is calculated as the positive difference between the strike price and the current stock price, indicating how much benefit the holder would gain if the option were exercised immediately.

Time Value

Time value is the additional premium an option has above its intrinsic value, reflecting the potential for further favorable movements in the underlying asset's price before expiration. It accounts for elements such as volatility and the remaining time until the option’s maturity.

American Option

An American option is a financial derivative that gives the holder the right, but not the obligation, to exercise the option at any point up to and including its expiration date. This flexibility means that American options, unlike European options, can be exercised early, which is particularly important for options that may be more valuable if exercised before maturity due to dividends or interest rate considerations.

Put Option

A put option is a type of option contract that grants the holder the right to sell an underlying asset at a specified strike price. It is typically used either to hedge against a decline in the value of the asset or to speculate on the downward movement of the asset's price.

Binomial Option Pricing Model

The binomial option pricing model is a discrete-time method used to evaluate options by simulating possible future price movements of the underlying asset over a series of time steps. It is particularly useful for pricing American options as it naturally incorporates the possibility of early exercise at each step.

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