Exam 18: Path-Independent Exotic Options

You have written a put on a put, where the underlying put is written on a stock index. To delta hedge yourself you can either go the underlying put or the underlying index.

A US-based investor buys from you a quanto option in which the payoffs from a euro-denominated call on a German company are converted back into US dollars at the fixed rate of $1.25/€. To hedge this transaction

Option prices are homogeneous of degree one in stock price and strike price. What does this imply?

The gamma of a cash-or-nothing binary call option is generally when the option is out-of-the-money and generally when it is in-the-money.

The delta of a cash-or-nothing call option is highest when the option is

In comparing a chooser to its straddle counterpart, which of the following statements is not valid?

A stock is trading at 100. Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ , respectively. The gross risk-free rate of interest per time step is 1.04. You are long a cash-or-nothing digital call option that pays $100 if $S _ { T } \geq 100$ , and nothing otherwise; and short a cash-or-nothing digital put option that pays $100 if $S _ { T } \leq 100$ , and nothing otherwise. (Here, $S _ { T }$ is the stock price at the end of two periods.) The value of your portfolio is

A compound option is

Consider the following compound options written on an underlying stock. Which one decreases in value when the stock falls in price?

An exotic option is

A quanto option is sometimes called a "wrong-currency" option because the payoffs of the quanto

Consider a stock that pays no dividends. You hold a portfolio comprising an asset-or-nothing call and a cash-or-nothing put. The options share the same strike, and the cash-or-nothing put pays an amount equal to the strike price if the put finishes in-the-money. Your portfolio is equivalent to

A cash-or-nothing binary call option increases in value when the price of the underlying increases. The delta of such an option

You are interested in hedging a portfolio of bonds against a rise in interest rates. Which of the following approaches will be most suitable to your goal?

A path-independent option is

Let $K$ denote the strike of an asset-or-nothing call option and $S _ { T }$ the price of the underlying at maturity. The option is worth

A stock is trading at 100. Consider a two-period binomial model in which the stock price moves up or down each period by factors $u = 1.20$ and $d = 0.80$ , respectively. Suppose the gross risk-free rate of interest per time-step is 1.04. In this setting, the price of a two-period cash-or-nothing binary put option with a strike of 100 that pays $100 if it finishes in-the-money is

You are long a portfolio of vanilla call options. Which of the following will help you hedge away your convexity (gamma)?

At maturity in an asset-or-nothing option written on a stock,

The delta of a cash-or-nothing binary call option and the gamma of such an option