The current price for a non dividend paying stock is currently $50.$ Expected annual rate is $10\%$ with continuous compounding interest rate. And a volatility of $20\%$ per annum. The stock price development during the next twelve months follows a binomial process with a period length of $6$ months. The annual riskless rate of interest is $5\%$ for all maturities. The stock is an underlying asset to an American call option, a out option and a futures contract. Both options have a strike price of $48$ and all three have a maturity in $12$ months.

Determine the current future price

Determine the call option value

Determine tge put option value

Calculate the put option gamma

Calculate the put option delta