A stock price is currently 40. It is known that at the end...

A stock price is currently $$\$ 40$$. It is known that at the end of 1 month it will be either $$\$ 42$$ or $$\$ 38$$. The risk-free interest rate is $8 \%$ per annum with continuous compounding. What is the value of a 1-month European call option with a strike price of $$\$39$$?

Key Concepts

Binomial Option Pricing Model

The binomial option pricing model is a simplified method for evaluating derivative securities by modeling the evolution of an asset’s price over time through discrete up and down movements. It breaks down the option’s life into a tree of possible outcomes and uses these outcomes to compute the option's fair value.

Risk-Neutral Valuation

Risk-neutral valuation is a fundamental concept used in financial economics where asset payoffs are expected under a probability measure that assumes investors are indifferent to risk. This allows for discounting expected future cash flows at the risk-free rate, simplifying the pricing of derivatives by equating them to their expected present values.

European Call Option

A European call option is a type of derivative that grants the holder the right, but not the obligation, to purchase an underlying asset at a specified strike price only at the option's expiration date. Its pricing involves calculating potential payoffs at expiration based on the asset's price movements and discounting them back to the present value.

Strike Price

The strike price, or exercise price, is the predetermined price at which the holder of an option can buy or sell the underlying asset when the option is exercised. In pricing options, the strike price is critical as it determines the intrinsic value of the option at expiration.

Continuous Compounding

Continuous compounding is an advanced method of calculating the present value of future cash flows, where the compounding period is considered to be infinitely small. It is widely used to discount cash flows in financial models, including the pricing of options, ensuring a more accurate reflection of the time value of money.

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