QUESTION $1$

$1.$ The pattern of volatility across exercise prices is often called

the price$-$fluctuation graph

the volatility smile

the skew

the term structure of implied volatility

QUESTION $2$

$1.$ The binomial price will theoretically equal the Black$-$Scholes$-$Merton price under which of the following conditions?

when the number of time periods is larg

when the option is at$-$the$-$money

when the option is in$-$the$-$money

when the option is out$-$of$-$the$-$money

QUESTION $4$

$1.$ The difference in profit from an actual put and a synthetic put is

X $$ ST

ST $+$ X$(1+$ r$)-$T

ST $$ X

none of the above

QUESTION $5$

$1.$ A covered call writer who prefers even less risk should

switch to a call with a lower exercise price

get rid of the call

get rid of the stock

switch to a call with a higher exercise price

QUESTION $6$

$1.$ Determine the appropriate price of a European put on a futures if the call is worth $$6\mathrm{.}55,$ the continuously compounded risk$-$free rate is $5\mathrm{.}6$ percent, the futures price is $$80,$ the exercise price is $$75,$ and the expiration is in three months.

$$12\mathrm{.}56$

$$1\mathrm{.}62$

$$0\mathrm{.}54$

$$11\mathrm{.}48$

QUESTION $7$

$1.$ A contango market is consistent with

futures prices exceeding spot prices

all of the above

a positive cost of carry

a negative basis

QUESTION $8$

$1.$ Find the forward rate of foreign currency Y if the spot rate is $$4\mathrm{.}50,$ the domestic interest rate is $6$ percent, the foreign interest rate is $7$ percent, and the forward contract is for nine months.

$$4\mathrm{.}532$

$$5\mathrm{.}104$

$$4\mathrm{.}468$

$$4\mathrm{.}458$

QUESTION $9$

$1.$ If a firm is planning to borrow money in the future, the rate it is trying to lock in is

the difference between the spot rate and the forward rate

the current spot rate

the forward rate at the termination of the hedge

the current forward rate

QUESTION $10$

$1.$ Suppose you observe the spot euro at $$1\mathrm{.}38/$ and the three month euro futures at $$1\mathrm{.}379/.$ Based on carry arbitrage, you conclude

this futures market is indicating that the spot price is expected to fall

this futures market is inefficient because the futures price is below the spot price

the risk$-$free rate in Europe is higher than the risk$-$free rate in the U$.$ S$.$

the spot price is too high relative to the observed futures price

QUESTION $11$

$1.$ Explain each of the following concepts as they relate to call options.

a$.$ Delta

b$.$ Gamma

c$.$ Rho

d$.$ Vega

QUESTION $12$

$1.$ Assume that there is a forward market for a commodity. The forward price of the commodity is $$120.$ The contract expires in one year. The risk$-$free rate is $10$ percent. Now, six months later, the spot price is $$140.$ What is the forward contract worth$($Value$)$ at this time?