Point to Remember 34

[Avishek]

Which of the following has the same impact on both American call and put option prices?


I. An increase in volatility.
II. An increase in the stock price.
III. An increase in the risk-free rate.
IV. A decrease in time to expiration.

A) I only.

B) I and II.

C) I and III.

D) I and IV.



Your answer: D was correct!

Increased volatility positively influences put and call option values, while a decrease in time to expiration will negatively influence call and put prices. Note that an increase in the stock price and an increase in the risk-free rate will cause the price of an American call to increase but will cause the price of an American put to decrease.

 

[Avishek]

The pricing results of the Black-Scholes-Merton model can be derived by:

A) lengthening the periods in the binomial model.

B) using a regression model of prices on volatility.

C) solving a system of simple mathematical equations.

D) taking the limit as the periods in the binomial model become shorter.



Your answer: D was correct!

As the option period is divided into more/shorter periods in the binomial option-pricing model, we approach the limiting case of continuous time and the binomial model results converge to those of the continuous-time Black-Scholes-Merton option pricing model.

 

[Avishek]

Which of the following statements is the reason that dividends complicate the pricing of an American call option?

A) Early exercise is always optimal, since upon exercise, the option owner captures the dividend.

B) The early exercise decision is complicated because of the reduction of the stock price following a dividend payment.

C) Estimating volatility on a dividend-paying stock is very difficult.

D) Dividends are too difficult to estimate over the life of the option.



Your answer: B was correct!

When a stock pays a dividend, it is implied that the price of the stock decreases. If the dividend is large enough, it can alter the payoff profile of an option purchased on that stock.

 

[Avishek]

A stock that is currently trading at $50 and can either move to $55 or $45 over the next 6-month period. The continuously compounded risk-free rate is 2.25 percent. What is the risk-neutral probability of an up movement?

A) 0.5566.

B) 0.6655.

C) 0.6565.

D) 0.5656.



Your answer: A was correct!


The risk-neutral probability, p, can be calculated as [e(rT)-d] / [u-d]. In this case, r = 0.0225, u = 1.1, d = 0.9, which makes p equal to [e[0.0225*(6/12)] - 0.9] / [1.1 - 0.9] = .5566

 

[Avishek]

The implied volatility of interest rates can be best computed using the market price of an:

A) interest rate forward contract.

B) interest rate call option contract.

C) interest rate futures contract.

D) S&P;500 option contract.



Your answer: B was correct!

Implied volatility of interest rates can be best computed using interest rate option contracts. Forward or futures contract pricing models do not have interest rate volatility as an input. S&P;500 option contracts have the volatility of the S&P;500 index (and not interest rates) as an input.

 

[Avishek]

Which of the following is TRUE for an option's price? An option's price is:

A) an increasing function of the underlying asset's volatility.

B) a decreasing function of the underlying asset's volatility.

C) unaffected by changes in the underlying asset's volatility.

D) a decreasing function of the underlying asset's volatility when it has a long time remaining until expiration and an increasing function of its volatility if the option is close to expiration.



Your answer: D was incorrect. The correct answer was A) an increasing function of the underlying asset's volatility.

Since an option has limited risk but significant upside potential, its value always increases when the volatility of the underlying asset increases.

 

[Avishek]

If we use four of the inputs into the Black-Scholes-Merton option-pricing model and solve for the asset price volatility that will make the model price equal to the market price of the option, we have found the:

A) historical volatility.

B) market volatility.

C) option volatility.

D) implied volatility.



Your answer: D was correct!

The question describes the process for finding the expected volatility implied by the market price of the option.

 

[Avishek]

Which of the following statements regarding the Black-Scholes-Merton option-pricing model is TRUE?

A) The Black-Scholes-Merton option-pricing model is the discrete time equivalent of the binomial option-pricing model.

B) The Black-Scholes-Merton model is superior to the binomial option-pricing model in its ability to price options on assets with periodic cash flows.

C) As the number of periods in the binomial options-pricing model is increased toward infinity, it converges to the Black-Scholes-Merton option-pricing model.

D) As the periods in the binomial option-pricing model are lengthened, it converges to the Black-Scholes-Merton option-pricing model.



Your answer: C was correct!

As the option period is divided into more/shorter periods in the binomial option-pricing model, we approach the limiting case of continuous time and the binomial model results converge to those of the continuous-time Black-Scholes-Merton option pricing model.

 

[Avishek]

Which of the following methods is NOT used for estimating volatility inputs for the Black-Scholes model?

A) Models of changing volatility.

B) Using long term historical data.

C) Using the most current historical data.

D) Using exponentially weighted historical data.



Your answer: A was correct!

The volatility is constant in the Black-Scholes model.

 

[Avishek]

Crashophobia is often attributed to the:

A) U.S. stock market crisis of 1987.

B) Asian currency crisis of 1997.

C) Long-Term Capital Management systemic crisis of 1998.

D) Latin American sovereign debt crisis of 1990.



Your answer: A was correct!

The term crashophobia is attributed to Rubinsteins explanation for the observance of a volatility smirk in implied volatility exhibited by equities. Implied volatilities are higher for low strike price puts because traders want to protect themselves against another substantial drop in the market.

 

[Avishek]

The buyer of a straddle on a stock is most likely to benefit:

A) if the volatility of the underlying assets price decreases.

B) if the position expires worthless.

C) under all conditions because the straddle is guaranteed a risk-free rate of return.

D) if the volatility of the underlying assets price increases.



Your answer: D was correct!

The buyer of the straddle purchases both a call and a put. This position will benefit from large swings of the price of the underlying stock in either direction. If the position expires worthless, which occurs when the stock price stays flat, the investor will lose 100% of the investment.

 

[Avishek]

An investor owns a stock and believes that the stocks price will remain relatively unchanged for the short term but is bullish in the long term. Which of the following strategies will be the best for this investor?

A) A covered call.

B) A protective put.

C) An at-the-money strip.

D) An at-the money strap.



Your answer: A was correct!

A covered call strategy is used to generate cash on a stock position that is not expected to increase in value over the life of the option.

 

[Avishek]

A financial intermediary that has credit risk as the primary risk exposure is a:

A) hedger.

B) packager.

C) market maker.

D) financial engineer.



Your answer: C was correct!

A market maker attempts to buy and sell the same option but retains the credit risk on each side of the transaction.