option expires worthless and no premium is due͘ Note that the net payoff for the option holder can be negative

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ϭ. [ϭϳ poinƚƐ΁ Use binomial lattices to find the premium on a pay later option on a stock with a current price of ΨϱϬ, a strike price of Ψϱϯ, and a volatility of ϯϬй. Assume a risk-free rate of ϱй. Assume the option is European style and the payoff is: �ሺ�், �ሻ ൌ ൜ �் െ � െ �, �் ൒ � 0, ��ℎ������ where, ST is the stock price at maturity, K is the strike price, and P is the option premium (for which you are solving). Note: A pay later option can be described as follows: ͞an option in which no premium is paid up front when the contract is entered͘ If the option is in the money at expiration, the option must be exercised and a premium is paid to the writer͘ Otherwise, the option expires worthless and no premium is due͘ Note that the net payoff for the option holder can be negative, when the option is not deeply in the money, so that the payoff is smaller than the premium͖ therefore by no arbitrage arguments, if the net payoff were always nonͲnegative, we could not have a contract with zero value at time t с Ϭ͘͟ HINT͗ You will need to use a method to solve for a nonlinear equation such as the Bisection method to solve this problem͘ Essentially you want to guess at premium values to set the initial value of the option to njero͘ ;I have populated the R vignette with a bisection code that will workͿ͘

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