3. A bear spread payoff has the form g(ST) = max(K₂- ST, 0) - max(K₁ – ST, 0), where 0 < K₁ < K₂. (a) (b) Sketch the payoff diagram. Use the general formula for the European option pricing function to find the time-zero option price of a bear spread.
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- The premium on a call option is primarily a function of the difference in spot price S relative to the strike price X, the length of time until expiration T, and the volatility of the currency o. C = f(S-X, T, o) For each characteristic of a call option, use the table to indicate whether that would lead to a higher call option premium or a low call option premium (all else equal). Characteristic A lower spot price relative to the strike price A shorter time before expiration A higher level of volatility for the currency Higher Call Option Premium O Lower Call Option Premium When using a call option to hedge payables in an international currency, a U.S. based MNC can lock in the to obtain the needed foreign currency. maximum minimum amount of dollars neededConsider the Black-Scholes model. In class, we derived the formula for the price of the European Call option. (a) Using the formula for the European Call option, calculate the Greek Delta. (b) Using the formula for the European Put option, calculate the Greek Delta.The premium on a put option is primarily a function of the difference in spot price S relative to the strike price X, the time until maturity T, and the volatility of the currency o. P = f(S-X, T, o) For each characteristic of a put option, use the table to indicate whether that would lead to a higher put option premium or a lower put option premium (all else equal). Characteristic A lower spot price relative to the strike price A shorter time before expiration A higher level of volatility for the currency Higher Put Option Premium Lower Put Option Premium When using a put option to hedge receivables in an international currency, a U.S. based MNC can lock in the receive. minimum maximum amount of dollars it will
- Consider a two-factor Arbitrage Pricing Theory (APT) model, T; = a; + b1,ifı + b2.i f2 + €i, with the following information Asset i Asset 1 0.07 0.50 0.25 Asset 2 0.15 1.10 0.75 Asset 3 0.20 b1,3 Hi b1i b2i 1.0 and the risk-free rate rp is 0.025. (a) Find the value of b13 to preclude arbitrage opportunity. (b) is an Asset 4 with 4 = 0.13, b14 = 0.8, and b2.4 = 0.4. Explain how you would exploit an arbitrage opportunity if thereUse the put-call parity relationship to demonstrate that an at-the-money call option on a nondividend-paying stock must cost more than an at-the-money put option. Show that the prices of the put and call will be equal if S0 = (1 + r)T..2. Derive the single - period binomial model for a put option. Include a single - period example where: u = 1.10, d = 0.95, Rf = 0.05, SO = $100, X = $100. 3. Assume ABC stock's price follows a binomial process, is trading at SO = $100, has u 1.10, d = 0.95, and probability of its price increasing in one period is 0.5 (q = 0.5). a. Show with a binomial tree ABC's possible stock prices, logarithmic returns, and probabilities after one period and two periods. . b. What are the stock's expected logarithmic return and variance for 2 periods and 3 periods? c. Define the properties of a binomial distribution.
- For each of the following option positions state the risk profile, draw the profit and loss area and show the breakeven price on each graph. a) Long 7.00 call @ 0.30 b) Short 7.00 call @ 0.30 Risk profile: Risk profile: c) Long 7.00 put @ 0.20 d) Short 7.00 put @ 0.20 Risk profile: Risk profile:fill the missing words: a. For ( ) options, when the spot price is ( ) than(or equal to)the exercise price, then profit/loss equals the premium. b. For ( ) options, when the spot price is ( ) than (or equal to) the exercise price, then the profit/loss will be equal to the option premium.In the context of single period binomial option pricing model with p*d = 0.75 and rf = 0.25 the values of the state price must be equal to A. PV$1u = $0.20 and PV$1d =$0.60 B. PV$1u = $ 0.25 and PV$1d = $0.50 C. PV$1u = $0.20 and PV$1d = $0.50 D. PV$1u = $0.60 and PV$1d =$0.20
- Consider a call and a put options with the same strike price and time to expiry. Given that the strike price is exactly equals to the forward price, then: A. Put and call have same premium B. The premium of the put is equal to the forward price C. The premium of the put is equal to the premium of the call plus the present value of the strike D. The premium of the call is equal to the forward price4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.In binomial approach of option pricing model, fourth step is to create : a. equalize domain of payoff b. equalize ending price c. riskless investment d. high risky investment
