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Call option:
A call option is an agreement where the buyer is entitled to a right to buy a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the call option is provided is called the underlying asset.
Put option:
It is an agreement where the buyer is entitled to a right to sell a stock at a pre-specified price (known as exercise price or strike price) within a pre-specified period. The stock on which the put option is provided is called the underlying asset.
Hedge ratio:
A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.
To compute:
The hedge ratio when the exercise price is
- $120
Determine the impact of more in the money on hedge ratio.
Answer to Problem 7PS
The hedge ratio is
When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.
Explanation of Solution
(a)
In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either
Given:
Calculation:
(b)
Call option:
A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.
Put option:
A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.
Hedge ratio:
A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.
To compute:
The hedge ratio when the exercise price is
$110
Determine the impact of more in the money on hedge ratio.
Answer to Problem 7PS
The hedge ratio is
0.33
Explanation of Solution
In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either
Given:
Calculation:
(C)
Call option:
A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.
Put option:
A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.
Hedge ratio:
A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.
To compute:
The hedge ratio when the exercise price is
$100
Determine the impact of more in the money on hedge ratio.
Answer to Problem 7PS
The hedge ratio is
0.67
When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.
Explanation of Solution
In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either
Given:
Calculation:
(D)
Call option:
A call option is an agreement that gives the buyer the right to buy a stock at a pre-specified price within a pre-specified period. The stock on which the call option is provided is called the underlying asset.
Put option:
A put option is an agreement that gives the buyer the right to sell a stock at a pre-specified price within a pre-specified period. The stock on which the put option is provided is called the underlying asset.
Hedge ratio:
A hedge ratio indicates the level of exposure of an investment to risk. For example, if a hedge ratio for an investment is 0.60 or 60%, it means 60% of that investment is protected from risk and remaining 40% of the investment is exposed to risk. A hedge ratio is calculated by dividing the option price range by the stock price range.
To compute:
The hedge ratio when the exercise price is
- $120
- $110
- $100
- $90 and
Determine the impact of more in the money on hedge ratio.
Answer to Problem 7PS
1
When the option becomes progressively more in the money, the value of the hedge ratio increases. It indicates that it is possible to protect the investment more, when the option becomes progressively more in the money.
Explanation of Solution
In the given case, stock price is $100. Up parameter (u) is 1.2 and down (d) is 0.9. So, after one year stock price may be either
Given:
Calculation:
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Chapter 21 Solutions
EBK INVESTMENTS
- 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.arrow_forwardDraw the profit diagram (profit not payoff) of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. Clearly state any assumptions made. Is the cost of the portfolio positive?arrow_forwardDifferentiate among the expected rate of return (r⁄), the requiredrate of return (r), and the realized, after-the-fact return (r) on astock. Which must be larger to get you to buy the stock, r⁄or r?arrow_forward
- We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity theorem as well as a numerical example to prove your answer.arrow_forwardAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) = ???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)arrow_forwarda) Carefully draw the payoff diagram of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. What reasons could a speculator have for holding such a portfolio (explain in detail)? b) Draw the profit diagram of the portfolio above (and clearly state any assumptions you make). Recall that the profit is equal to the difference between the payoff of the portfolio at expiry (maturity) date and the cost of the portfolio. Is the cost of the portfolio positive?arrow_forward
- We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of the put?b. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio?c. What is the present value of the portfolio?d. Given that the stock currently is selling at 100, solve for the value of the put.arrow_forwardExplain in detail with an example how the change of the variables (like Stock Price, Exercise Price, Risk-Free Rate, Volatility or Standard Deviation, and Time to Expiration) of Black-Scholes-Merton Formula affect the price of the option.arrow_forwardWhat impact does each of the followingparameters have on the value of a call option?(1) Current stock pricearrow_forward
- Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is foundto be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the requiredreturn on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B(B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to payreturns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standarddeviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also hasstandard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whetherasset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (??) =???????, where ??,?? are standard deviations of asset i and marketportfolio, ??? is the correlation between asset i and the market portfolio)Question 2. Foreign exchange marketsStatoil, the national…arrow_forwardWhich of the following is true: The BSM model combined with the put call parity can be used to give the theoretical price of an American put option. One of the variables that influences the price of the option is the expected return on the stock. Since dividends could trigger an early exercise of an American call, the BSM formula dividend adjustment will provide the correct price of an American call. The BSM formula requires cumulative probabilities from the lognormal distribution. The BSM model may be used with currency options by replacing the dividend yield with the foreign interest rate.arrow_forwardQuestions C and D is required. c) Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (A) to beta of B (B). d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i ( , where are standard deviations of asset i and market portfolio, is the correlation between asset i and the market portfolio)arrow_forward
Intermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning