Calculate the value of the following call and put options by using of Binomial Option Pricing Model $(25$ marks$)$

Type of option A call or a Put options with exercise price of $$40,$ maturity is $1$ year

Price changes Assume that the price changes $3$ times per year

Price volatility Assume that the volatility of the stock is $25\%$

Probability Up $50\%$

Down $50\%$

Risk$-$free interest rate $15\%$ per year

Face value of sukuk

Left to Maturity

Exercise Price

Current price of the stock

$6-$Month LIBOR

USD $10000$

$6$ months

USD $50$

USD $55$

$8\%$

Estimated stock's price volatility $25\%$

What is the value of the above embedded call option according to Black$-$Scholes Option Pricing Model? $(25$ marks$)$