Question 44 of 45

In a one-period binomial model the underlying price S0 = 50. After the period it will be either S1_u = 65 or S1_d = 40. A European call with strike X = 55 expires at period end. If the risk-free rate for the period is 2 percent, what is the hedge ratio h for a short call position replicated by buying h units of the underlying?

A stock S0 = 80 will be either 110 (up) or 60 (down) next period. A call with X = 100 has payoffs 10 and 0 in the states. If r = 5 percent, what is the risk-neutral probability pi of an up move?

True or false: In the one-period binomial model, the actual real-world probability q of an up move affects the no-arbitrage option price.

Stock S0 = 100 is expected to go to either 130 or 70. Consider a put with X = 90 and r = 0. What is the put payoff vector (p1_u, p1_d)?

A put's payoffs are (0, 20) as in Question 5. With pi = 0.58333 and r = 5 percent, what is the put price p0?

Which of the following statements best describes why put and call prices derived from the one-period binomial model do not require investors' risk preferences?

Stock S0 = 16 moves to either 20 or 12. If r = 5 percent, what is the risk-neutral probability pi?

In a one-period model, increasing the spread between Ru and Rd while keeping S0 and r fixed will generally:

You sell a call and buy h units of the underlying to form a risk-free portfolio. If V1 is the common payoff in both states and r is the period rate, which equation gives c0 (call price)?

If a call option is overpriced relative to the binomial no-arbitrage price, an arbitrageur should:

Which of the following is a correct expression of the hedge ratio for any derivative whose value at expiry depends only on the underlying price in the two states?

Given S0 = 120, S1_u = 150, S1_d = 90, X = 110, r = 4 percent. A call's payoffs are (40, 0). Compute c0 using risk-neutral pricing.

If the risk-free rate increases while Ru and Rd remain unchanged, which of the following is typically true for European calls and puts (other things equal)?

A derivative has payoffs c1_u = 30 and c1_d = 5. Under S1_u = 150 and S1_d = 100 and S0 = 120, what is the hedge ratio h?

Which of the following best explains why replication pricing yields the same option price as discounted risk-neutral expected payoff?

If a one-period binomial model gives h = 0.2 and S0 = 80 and the common payoff V1 = 12 with r = 5 percent, what is the call price c0?

A European call in a one-period model has c1_u = 12 and c1_d = 0. If S1_u = 132, S1_d = 88 and S0 = 110, what is h?

Which factors determine the risk-neutral probability pi in a one-period binomial model?

Consider S0 = 300, S1_u = 360, S1_d = 240, X = 320, r = 0. What is the call's up and down payoff vector (c1_u, c1_d)?

If the hedged portfolio yields V1 = 50 in both states and r = 10 percent, what is present value V0 used in replication pricing?

A trader constructs a synthetic long underlying by combining a long call, short put (same X and T) and lending PV(X). Which parity principle justifies this?

In a one-period binomial model, if S0 = 50, Ru = 1.4, Rd = 0.8, and r = 5 percent, what is Ru - Rd?

Which of the following is NOT required to compute the no-arbitrage price of a European option in a one-period binomial model?

You observe a call priced below its binomial no-arbitrage value. Arbitrage strategy to exploit this mispricing is to:

A one-period call has c1_u = 8, c1_d = 1. Under S1_u = 120, S1_d = 80, S0 = 100, r = 2 percent. What is the hedge ratio h?

Which statement about multi-period extension of the one-period binomial model is correct?

When forming a hedged portfolio by selling one call and buying h shares, the portfolio is risk-free because:

If a put is overpriced in the market relative to its binomial no-arbitrage price, an arbitrageur should:

Which of the following increases the risk-neutral probability pi for an up move, holding Ru and Rd constant?

Why does increasing Ru and decreasing Rd (wider up/down moves) raise both call and put prices?

A protective put portfolio equals which of the following at inception according to put-call parity?

If S0 + p0 > c0 + PV(X) in the market, an arbitrageur should:

A stock S0 = 295, forward price F0(T) = 300.84, r and T such that PV(X)=295. Which statement about a call and put with X = F0(T) is correct today?

You calculate a put price via binomial model as 6.20. Market put trades at 7.00. Which elementary arbitrage is suggested by the chapter?

Which statement about the hedge ratio h is correct as option goes deeper in-the-money (all else equal)?

Given S0 = 50, S1_u = 75, S1_d = 25, a call with X = 60 has payoffs (15, 0). If r = 0 and you short the call and buy h underlying to hedge, what is V1 (common payoff) you will obtain?

If option c0 equals 4.57 as earlier example and S0 = 80, h = 0.2, what is current value of hedged portfolio V0?

A one-period model yields pi = 0.48. Option payoffs are c1_u = 10 and c1_d = 0. With r = 5 percent, what is c0?

A stock pays no dividends. If you observe a call and put with same X and T, which parity holds that links calls, puts, underlying, and bond?

A trader wants to replicate a sold call when exercise is certain at maturity. Which replication matches the sold-call payoff according to the chapter?

You price a call using replication and obtain c0 = 5.00. Using put-call parity with S0 = 50 and PV(X) = 45, what should the put p0 equal?

If an option's time-to-expiration shortens (T decreases) while other inputs unchanged, what is the typical effect on option time value?

A bank observes a one-period call price computed as 6 by the binomial model but market call is 8. If frictionless trading is possible, net initial cash flow from arbitrage by following correct strategy?

In the one-period binomial model, which of the following reasons explains why the underlying's expected return mu does not affect option price?