The current spot price of a stock is $100 per share, and the risk-free rate is 5%.

The stock pays no dividends and costs nothing to store.

The forward price is $105.

Each period the stock price either doubles (u=2) or halves (d=1/u=0.5)

Consider a LONG CALL position with a strike of $105 (at the money).

The system of two equations to replicate the payoff is as follows.

$95 = * $200 + B * $1.05

$ 0 = * $50 + B * $1.05

The solution to this system is.

= (95-0) / (200-50) = 95/150 = 19/30 or approximately 0.6333

B = (95 - * 200) / 1.05

= (95 19/30 * 200) / 1.05

Or -30.1587

Use and B to determine the premium on the call. Premium = $___ ___ . ___ ___

In class, we derived the formula for the risk-neutral probability.

q = (1+r-d) / (u-d)

Calculate q.

q = ___ ___ . ___ ___ ___ ___ %

Show how we use risk-neutral probability (q) and the risk-free rate (r) to calculate the premium on the call and verify your answer to question 1.

The equation for the Call premium is

________________________________________________________________________

The call premium based on the above equation is $___ ___ . ___ ___

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