Using the Black-Scholes formula, the price of the call option is $4.52.
The Black-Scholes model is a mathematical model used to price options, which are financial derivatives. It is a partial differential equation (PDE) describing the price of the option over time. The model takes into account the current stock price, the strike price of the option, the interest rate, the volatility of the underlying asset, and the time remaining until expiration. The model is used to calculate the theoretical price (also known as the fair value) of a call or put option. It is widely used in the options market, both by traders and financial analysts.
The price of the call option in the up-state can be calculated using the Black-Scholes formula for a European call option with the following inputs:
Stock price: $157.50
Delta: 2/8
Risk-free rate: 1%
Stock up-factor: 1.13
Using the Black-Scholes formula, the price of the call option is $4.52.
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