For a binomial model for the stock prices, you are given:
Each period is one year.
The current price for a nondividend-paying stock is $50.
u=1.2, where u is one plus the rate of capital gain on the stock per period if the stock price goes up.
d=0.8, where d is one plus the rate of capital loss on the stock per period if the stock price goes down.
The current price of a one-year at-the-money European put option on the stock is $3.253.
Calculate the current price of a two-year at-the-money European call option on the stock.
When I apply u = 1.2 = e^(r+sigma) and .8 = e^(r-sigma). Subtracting the two equations results in 2(sigma) = .40567 therefore sigma = .20273. Plugging back in results in a negative r which isnt possible. So clearly this method is wrong and the way to solve this is directly plug in the p* formula and solve for r, since the price of the put is given. Once we know r, we can solve for the price of the call.
Why can't we use u and d to solve for sigma and r. Does it have something to do with "one plus rate of the capital gain/loss on the stock"?
Each period is one year.
The current price for a nondividend-paying stock is $50.
u=1.2, where u is one plus the rate of capital gain on the stock per period if the stock price goes up.
d=0.8, where d is one plus the rate of capital loss on the stock per period if the stock price goes down.
The current price of a one-year at-the-money European put option on the stock is $3.253.
Calculate the current price of a two-year at-the-money European call option on the stock.
When I apply u = 1.2 = e^(r+sigma) and .8 = e^(r-sigma). Subtracting the two equations results in 2(sigma) = .40567 therefore sigma = .20273. Plugging back in results in a negative r which isnt possible. So clearly this method is wrong and the way to solve this is directly plug in the p* formula and solve for r, since the price of the put is given. Once we know r, we can solve for the price of the call.
Why can't we use u and d to solve for sigma and r. Does it have something to do with "one plus rate of the capital gain/loss on the stock"?
Basic Binomial Tree question
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