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Suppose the current stock price is 30 . In one year, the stock will either go up to 36 or down to 25 . The stock pays no dividends and the risk-free rate is 4%. Using a one-period binomial tree, the delta Δ of a put option with strike price K is -0.63636 .

a) Find the strike price K.
b) Find the put premium.

1 Answer

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Final answer:

In a one-period binomial tree, the delta of a put option calculates the sensitivity of the option price to changes in the stock price. The strike price K can be calculated using the formula K = current stock price - Delta * current stock price. The put premium can be calculated using the formula put premium = delta * (up move in stock price - down move in stock price) * risk-free rate.

Step-by-step explanation:

In a one-period binomial tree, the delta Δ of a put option at the current stock price of 30 is -0.63636. The delta of a put option represents the sensitivity of the option price to changes in the stock price. Since the delta is negative, it indicates that the put option price will decrease as the stock price increases.

To find the strike price K, we can use the formula: K = current stock price - Delta * current stock price. Substituting the values, we get K = 30 - (-0.63636) * 30 = 30 + 19.0908 = 49.091.

To find the put premium, we need to use the formula: put premium = delta * (up move in stock price - down move in stock price) * risk-free rate. Substituting the values, we get put premium = -0.63636 * (36 - 25) * 0.04 = -0.63636 * 11 * 0.04 = -0.27999744.

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