PRM Certification 8006 Dumps PDF

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.)

All the statements are correct, and represent the relationships between the values of the Greek variables for calls and puts for the same option. It is important to know why as the PRM exam often asks tough questions about the Greeks.

Statement I is correct because of the put-call parity. According to the put-call parity,

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

Now the delta of the spot is 1, and that of the discounted price is zero. Therefore

Delta of Call - Delta of Put = 1 - 0, or by rearranging we get the equation in statement I.

Statements II and III are correct as the gamma and vega of both the spot price and the discounted price are zero. Therefore using the put-call parity, we can say

Gamma of Call - Gamma of Put = 0 - 0, and

Vega of Call - Vega of Put = 0 - 0

Rearranging, we get statements II and III.

Statement IV is correct because of the following relationship between theta of call and theta of put:

Theta of Put = Theta of Call + rKe^(-rt).

Since rKe^(-rt) can only be a positive number, theta of put can only exceed the theta of a call. However, since theta is generally negative, it often implies that the theta of a call is the larger absolute number.

Additional explanation for the last point: Assume rKe^(-rt) =+1 and theta of a put is -5 (completely hypothetical)

Now Theta of Put = Theta of Call + rKe^(-rt)

Ie -5 = -6 + 1

Now -5 is the larger number than -6. In other words, theta of put exceeds that of the call in a pure mathematical sense, which is what I mean when I say “theta of put can only exceed the theta of call”. But if you ignore the sign, then theta of call is larger at 6 when compared to 5. Therefore the theta of the put is greater than the theta of the call – which is what the answer says.

The LIBOR rate to use is the one at the beginning of the period, is 4.5%. The fixed rate payer owes 5%, and the floating rate payer owes 4.5% + 100bps. Thus the fixed rate payer will receive a payment equal to 0.5% for six months on $1m. This works out to $2500.(Recall that a fixed for floating interest rate swap exchanges fixed for floating rate payments, with only the net payment being made by either party.)

The LIBOR rate to use is the one at the beginning of the period, is 4.5%. The fixed rate payer owes 5%, and the floating rate payer owes 4.5% + 100bps. Thus the fixed rate payer will receive a payment equal to 0.5% for six months on $1m. This works out to $2500.

(Recall that a fixed for floating interest rate swap exchanges fixed for floating rate payments, with only the net payment being made by either party.)