Derivative

Question 1

Delta Hedged Portfolio - what is

Answer 1

Detal hedged porfolio consists of long position in stocks and short position in call options. Because the gamma of long stock position is zero and the gamma of short call is negative, the net gamma of a delta hedged portfolio is negative

Shares /delta = #of calls to short to hedge

Question 2

put-call parity formula - continuous compound

and regular

Answer 2

Po= Co - So + X/e^(Rf*T) = continuous
Po= Co - So + X/(1+Rf)^T

So + Po= Co + pvX

Po-Put price
Co-Call price
X-Exercise price
Rf- Risk Free rate
T-time in years to expiration

Question 3

Forward contract price formula

Answer 3

FP=So * (1+Rf)^T
So=Spot price
T= Forward contract term in years

Question 4

no arbitrage price of an equity forward contract

Answer 4

FP=(So-PVD) * (1+Rf)^T
or So*(1+Rf)^T - FVD

PVD - present value of dividends
FVD future value of the dividends

Question 5

Value of the long position in a forward contract on a dividend paying stock

Answer 5

=(St-PVDt) - FP/(1+Rft)^(T-t)

Question 6

Probabilities of an up move

Answer 6

Uprob= (1+Rf-D) / (U-D)

Question 7

Gamma Risk

Answer 7

Gamma risk arises when the price of the underlying jumps abruptly. Measures the rate of change in delta as the stock price changes

Long positions in calls and puts have positive Gamma
Gamma is highest for at-the-money options

Question 8

Vega

Answer 8

Measures the sensitivity of the option price to changes in the volatility of returns

Question 9

Rho

Answer 9

measures the sensitivity of the option price to changes in the risk free rate

Question 10

Theta

Answer 10

measure the sensitivity of the option price to the passage of time

Question 11

Protective Put

Answer 11

Long stock position and long put position

Question 12

Cash Secured Puts

Answer 12

writing a put options and deposition an amount equal to the put exercise price in a designated account.

Question 13

Finding forward rate of adjacent node

Answer 13

If up *e^(2 * volatility)

If down /e^(2 * volatility)

Question 14

FP = What

or how to calculate spot price

Answer 14

In the absence of an arbitrage opportunity, the value of should be 0.

Therefore, FP = S0(1 + Rf)T

Question 15

Value of a Call option

Answer 15

Call Value = Put Value − Xe^-rt + S =

$4.78 − $100.00e(−0.07 × 1.0) + 100 = $11.54

Question 16

FP (on an equity Index)

Answer 16

So x e ^[(Rf - Dy)T] = FP

Question 17

Limitations of BSM

Answer 17

The following are limitations of the BSM:

The assumption of a known and constant risk free rate means the BSM is not useful for pricing options on bond prices and interest rates.
The assumption of a known and constant asset return volatility makes the BSM not useful in situations where the volatility is not constant which occurs much of the time.
The assumption of no taxes and transaction costs makes the BSM less useful.
The BSM is designed to price European options and not American options.

Question 18

Bull Spread vs Bear

Answer 18

Can use calls or puts:

The exercise price of the long option is lower than the exercise price of the short option.

Bear is the reverse. The Exercise price of the long option is higher than the price of the short.