INV2601-Exam Oct_Nov 2023 (page 3 of 20)

Tick all those statements on options that are correct (and don't tick those statements that are incorrect). O a. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. Ob. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. 0 C. If interest is compounded continuously then the put-call parity formula is P+ S(0) = C + Ke where I is the expiry time. Od. In general the equation S(T) + (K − S(T))+ (S(T) — K)† + K is valid. An American put option should never be exercised before the expiry time. e. =

Problem 4d: State whether the following statements are true or false. In each case, provide a brief explanation. d. In a binomial world, if a stock is more likely to go up in price than to go down, an increase in volatility would increase the price of a call option and reduce the price of a put option. Note that a static position is a position that is chosen initially and not rebalanced through time.

Consider the Black-Scholes equation for the option price V(S, t) if the underlying does not pay out dividends. (i) Show that V(S,t) = AS, where S is the underlying price, t is time, and A is a constant, is a solution to the Black-Scholes equation. (ii) For the solution V(S,t) = AS, define the value A (Delta) used for hedging.

Which of the following describes delta? O The ratio of the option price to the stock price None of these O The ratio of a change in the option price to the corresponding change in the stock price The ratio of a change in the stock price to the corresponding change in the option price O The ratio of the stock price to the option price ◄ Previous Next ▸

Question 1 (Mandatory) Which of the following equations calculates a put option's value? Os.et. N(d2) - K N(da) OK.ert. N(d2) - S. N(d) Os.e*t. N(-d2) - K N(-dg) OK.et.N(-d2)- S N(-d1) Question 2 (Mandatory) The forward price is determined at contract initiation but changes during the life of the forward contract. O True False

Which of these will increase the value of a call option? I. An increase in the market value of the underlying asset II. An increase in the option's exercise (or strike) price III. A decrease in the market value of the underlying asset IV. An increase in the volatility of the underlying asset's returns A) I and Il only в) I only C) I and IV only D) Il and III only

2-2 What are the variaables in the BSM call option valuation model below and how do they affect call option pricing?

Tick all those statements on options that are correct (and don't tick those statements that are incorrect). a. The put-call parity formula necessarily requires the assumption that the share price follows a geometric Brownain motion. b. In general the equation S(T) + (K − S(T))† = (S(T) – K)+ + K is valid. An American put option should never be exercised before the expiry time. C. d. The Black-Scholes formula is based on the assumption that the share price follows a geometric Brownian motion. e. If interest is compounded continuously then the put-call parity formula is P + S(0) = C + Ke¯T where T is the expiry time.

6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)

Use 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 So = (1 + r)^T

8. Holding everything else equal, the increase in the volatility (variance) of the underlying stock will cause  A.value of a put option decreases and that of a call option increases. B.value of both a put option and a call option increase. C.value of a put option increases and that of a call option decreases. D.value of both a put option and a call option decrease.

6. Factors that affect the value of options Aa Aa Understanding how different factors affect the value of options is the first step to understanding option pricing models. The following table shows how increases in the given factors on the left affect the value of a put option. For each factor, indicate whether an increase in its value causes the value of the put option to increase or to decrease. Causes the Value of the Put Option To Increases in this factor: Increase Decrease Underlying stock price Exercise price Time to expiration Volatility Which of the following best describes a naked option? When an investor sells call options without the stock to back them up When an investor writes call options against stock held in his or her portfolio

Can you please help with the question in the picture attached? The answer should be only one and I’m quite confused. Thank you!

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4. Answer the following questions on exotic options: (a) Discuss the differences between a combination and a spread when constructing portfolios of options. (b) Define a long strangle and represent the profit function. (c) Design a forward contract on a stock with a particular delivery price and delivery date as a combination of options on the same underlying asset.

An increase in the volatility of returns of the underlying stock (and holding everything else constant):  A. Decreases both call and put option values B. Increases both call and put option values C. Increases put option values but not call option values D. Decreases call option values but not put option values E. Increases call option values but not put option values

Which of the following would increase the price of a put option on common stock , all else equal? I. Decrease in stock price II . Decrease in stock price volatility III . Decrease in time to maturity IV . Increase in exercise price II , and IV l and IV I only I III , and IV IV only

Describe the effect of a change in each of the following factors on the value of a calloption:1. Stock price2. Exercise price3. Option life4. Risk-free rate

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

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Please answer both QUESTION 7 According to the capital asset pricing model (CAPM), fairly priced securities should have A. A non-zero alpha. в.A fair return based on the level of systematic risk. C. A fair return based on the level of unsystematic risk. D.A beta of 1. QUESTION 8 Diversification can increase fair return. True False