PRMIA 8006 Exam I: Finance Theory, Financial Instruments, Financial Markets – 2015 Edition Exam Practice Test

Answer : B

The value of Bond 1 is $900,000 and the value of Bond 2 is $1,100,000, or their respective weights in the portfolio are 45% and 55% respectively. The combined duration is the weighted average of their individual durations, ie (45% x 5) + (55% x 10) = 7.75 years

Answer : B

Analytical methods are more 'efficient' than numerical methods in terms of computing power required, consistency of results and providing clarity on the inputs driving the results. Therefore 'efficient valuation' is not a reason to adopt numerical pricing methods over analytical methods.

It is much easier to incorporate changing stochastic volatility, discontinuous asset prices or other complex payoffs using numerical pricing methods. So these certainly represent good reasons to use numerical pricing methods for valuing exotics.

Therefore Choice 'b' is the correct answer.

Answer : A

Implied volatility is the volatility that is priced in the current market prices. In other words, we know the formula for pricing an option, and we find the value of the volatility for which we get the current market price. It is the volatility that the market is ascribing to that security. Therefore statement I is not correct.

Implied volatility in the market tends to vary across strikes, even with the same underlying. There is a certain level of demand for out of the money puts, for example, from investors trying to set a floor for their losses. At the same time, there is a natural supply of out of the money calls from investors trying to earn some relatively risk free premiums. These factors cause options with different strikes to be priced in a way as to give different estimates of market volatility at each strike *& resulting in the 'volatility smile'). Therefore statement II is not correct.

The shape of the implied volatility curve is called the 'volatility smile', because of the shape it sometimes takes. Statement III is correct.

Theta is the rate of change of an option's price with the passage of time. It causes the value of the option to decrease over time, such that if it is out of the money and close to expiry, the price of the option approaches zero. Theta is therefore negative by definition. Statement IV is not correct. Remember that theta will be positive for short positions.

Answer : C

Treasury bills are short-term government securities with maturities ranging from a few days to 52 weeks. Bills are sold at a discount from their face value, and do not carry a coupon.

Answer : B

Everything else remaining the same, an increase in the rate of dividends causes the value of call options to fall and the value of put options to rise. Therefore, Choice 'b' is the correct answer. (In the exam, the question could address either a call or a put option, so be aware of the answer in either case).

To understand this, consider how dividends are accounted for when valuing an option using the Black Scholes model. Future dividends are discounted to the present using the risk free rate and this discounted value is reduced from the spot price used in the BSM valuation. Effectively, this reduces the spot price used in the BSM formula. When the spot price reduces, and the exercise price remains the same, then the value of the call option goes down. In the same way, when spot price is reduced by the present value of dividends (and the exercise price stays the same), obviously the put option becomes more valuable. Therefore an increase in the rate of dividends increases the value of the put option.

There is another intuitive way to think about this: A call option is like a long position in the stock, but the holder of the call option is not entitled to receive dividends (unlike the holder of the stock). Since the holder of the call option has to forego the dividends, he is willing to pay less for the option; or in other words, the value of the call reduces.

In the same way, a put option is like having a short position in the stock. The holder of the short position has to borrow the stock in order to get into the short position in the first place. When dividends are paid, the holder of the short stock position has to make good any dividends that might be paid to the lender of the stock. The holder of a put option does not have to make any such payments. Therefore the put option is more valuable, and the existence of dividends (or an increase in dividends) increases the value of the put option.

(Try this out using the Black Scholes Excel model given under the tutorials by varying the spot price.)

Answer : A

We can use the put-call parity to estimate the value of the call option in this case.

The put-call parity can be expressed as:

Value of call - Value of put = Spot price - Exercise price discounted to the present

Substituting the values we know:

Value of call - $5 = $100 - $110/(1 + 10%); which implies the value of a call is also $5.

Choice 'a' is therefore the correct answer.

Note about interest rates: How do we know if the interest rate provided in the question is continuous or discrete? For short periods of time, the difference between discrete and continuous exchange rates tends to be not material. For ease of computation, use discrete rates (as above), and it should allow you to answer the question.

Answer : B

The relationship between the value of an option, and its delta, gamma and theta is given by rV = + rS + 0.5(S)2, where V is the value of the option, r the risk-free rate, S the spot price of the underlying, and , & are the respective Greeks.

For a delta neutral portfolio, = 0 and this equation reduces to rV = + 0.5(S)2. Now rV is generally a small number, which means that if is large and positive, must be large and negative to offset that. Therefore Choice 'b' is the correct answer.