Calculate the price of a two-month European put option given the following information: the exercise price is $19,the current share price is $15 and the risk-free interest rate is 12% p.a.Furthermore,the share price may go up by 10 per cent or down by 10 per cent at the end of each month.Assume a risk-neutral world and time periods of one month each.

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In a risk-neutral world, the expected return on the asset is the risk-free rate. To calculate the price of the put option, we use the binomial option pricing model. First, calculate the up and down factors: $u = 1.10$ and $d = 0.90$. The risk-neutral probabilities are calculated as $p = \frac{e^{r\Delta t} - d}{u - d}$, where $r$ is the risk-free rate, and $\Delta t$ is the time step (1/12 year for a month). With $r = 0.12$, we get $p = \frac{e^{0.12/12} - 0.90}{1.10 - 0.90} = 0.537$.Next, calculate the option value at each final node:- If the stock goes up twice, the put option is worthless (0).- If it goes up then down or down then up, the stock price is $15, and the put option value is $max(K - S, 0) = max(19 - 15, 0) = 4$.- If it goes down twice, the stock price is $15 \times 0.9 \times 0.9 = 12.15$, and the put option value is $max(19 - 12.15, 0) = 6.85$.Then, calculate the expected option value at the first node (one month to expiration) and discount it back to the present value:- The expected value if the stock goes up first is $0.537 \times 0 + (1 - 0.537) \times 4 = 1.848$.- The expected value if the stock goes down first is $0.537 \times 4 + (1 - 0.537) \times 6.85 = 5.2165$.The present value of the option is then calculated by taking the expected value of these two outcomes, weighted by the risk-neutral probabilities, and discounting back one period:$$PV = e^{-r\Delta t} \times (p \times 1.848 + (1 - p) \times 5.2165) = e^{-0.12/12} \times (0.537 \times 1.848 + 0.463 \times 5.2165) = 3.63.$$Therefore, the price of the two-month European put option is approximately $3.63.

Calculate the Price of a Two-Month European Put Option Given