Black–Scholes [LO2] What are the prices of a call option and a put option with the following characteristics?
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FUND. OF CORPORATE FIN. 18MNTH ACCESS
- KF1. Which statement is false? a All else being equal, options of the same strike will increase in price depending on the volatility of the underlying. b According to put-call parity, if a stock is trading for a price that is at-the-money, the put and the call should be trading at the same, or very close to, the same price. c A short put option is functionally the same as a long call option (it results in the same thing). d All statements are true e All statements are falsearrow_forwardConsider a world with only two risky assets, A and B, and a risk-free asset. The two riskyassets are in equal supply in the market, i.e., the market portfolio M = 0.5A + 0.5B. Itis known that R¯M = 11%, σA = 20%, σB = 40% and ρAB = 0.75. The risk-free rate is2%. Assume CAPM holds.(a) What is the beta for each stock?(b) What are the values for R¯A and R¯B?arrow_forward1. Consider a family of European call options on a non - dividend - paying stock, with maturity T, each option being identical except for its strike price. The current value of the call with strike price K is denoted by C(K) . There is a risk - free asset with interest rate r >= 0 (b) If you observe that the prices of the two options C( K 1) and C( K 2) satisfy K2 K 1<C(K1)-C(K2), construct a zero - cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage.arrow_forward
- 13. I just made this one up. To my knowledge, "Binarrier Options" don't exist, but maybe they do. A binary (a.k.a. digital, all-or-nothing) call option has a strike price of $51. It also has a knock-out barrier of $65. If the option pays you at expiration, it pays you exactly $10. The risk-free rate is 9.2% per period. If the underlying asset goes up, it will go up 20% per period and if it goes down, it will go down 10% per period. The underlying asset currently costs $50. The option expires in 2 periods. How much is this option worth today? Round to the nearest pennyarrow_forwardD4) Real options make up a lower proportion of the total value of ”value stocks” than “growth stocks” True False 2.In general, an option is more valuable when it is not available to anyone. True Falsearrow_forwardD3) Finance Consider an option with α being a non-negative parameter and the option pays ((S(T))α − K)+ at maturity date T. Let Cα(S(0), σ, r) be the risk neutral price of the option (with interest rate r and volatility σ) when the initial price is S(0). Obviously, C1(S(0), σ, r) = C(S(0), σ, r) is the price of an ordinary call option. Show that, Cα(S(0), σ, r) = e(α−1)(r+ασ2/2)TC((S(0))α, ασ, rα), where rα = α(r − σ2/2) + α2σ2/2.arrow_forward
- The risk-free rate is 4%. The expected market rate of return is 11%. If you expect CAT with a beta of 1.0 to offer a rate of return of 13%, you should A. buy CAT because it is overpriced. B. buy CAT because it is underpriced. C. None of the options, as CAT is fairly priced. D. sell short CAT because it is overpriced. E. sell short CAT because it is underpriced.arrow_forwardA4) Critically explain the risk premium of a zero-beta stock. Does this mean you can lower the volatility of a portfolio without changing the expected return by substituting out any zero-beta stock in a portfolio and replacing it with the risk-free asset?arrow_forward1) Why is writing a naked call option very risky ? ( find out first what a naked call is ) 2) Graph the profits and losses associated with writing a call option on a security with a strike price of $60 and a premium of $5.arrow_forward
- a) Suppose the risk-free rate is 7% and the expected rate of return on the market portfolio is 10%. In your view, the expected rate of return of a security is 12.2%. Given that this security has a beta of 1.4, do you consider it to be overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model? Please provide the details of your calculations b) explain when a security is overpriced, under-priced or fairly priced according to the Capital Asset Pricing Model.arrow_forward10. An announcement that the prices of goods and services in the market are risking would cause an increase in which of the following? O a. The default risk premium O o The risk free rate ) r The liquidity risk premium O o The inflation risk premiumarrow_forwardSuppose you observe the following situation: Security Beta Expected Return Peat Company 1.70 13.60 Re - Peat Company 0.85 10.80 Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk - free rate?arrow_forward
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