Quiz # 6

If S_T is the terminal spot price and is the strike price then the payoff from a covered call position is::


a) max (S_T ,K)
b) min (S_T ,K)
c) max (S_T ,K) -- min (S_T ,K)
d) max (S_T ,K) - S_T



Consider a one year at-the-money (ATM) digital option (with zero interest rates and dividends) and an ATM volatility of 30%. The volatility skew is 4% per 10% change in strike. A trader who ignores this skew will get the price of this digital option wrong by:


a) 10.45%;
b) 11.45%;
c) 12.00%;
d) 16.22%;



A trader trading a one year down barrier option (down and out call option) with a strike of 100 and a barrier of 90. The volatility is 30% and the barrier is continuously monitored. If the barrier has to be discretely monitored every day then the barrier will be at:


a) 86.5;
b) 87.6;
c) 88.6
d) 89.5



Roger Lee in a 2004 paper has shown that implied variance is:) The 30 year bond yield is 5% and the volatility of the 30 year yield is 8%, the two year note yield is 3.5% and the volatility of the two year note yield is 6.5%; the correlation between the two year and the 30 year yield is 0.65. The yield spread volatility is:


a)  1.67%
b) 7.82%
c) 2.35%
d) 0.31%



Suppose a trader sells a knock out call option with a barrier B and strike K such that B = K < S₀ where S₀ is the current stock price and charges a premium of S₀-K. He then hedges the position by buying one stock per option. If the interest rates and dividends are zero then this portfolio represents:


a) a capped call option;
b) a stop loss order;
c) a call spread;
d) none of the above;



If the barrier is equal to the current spot price then the value of a down and out call option will be:


a) one
b) zero
c) infinity
d) 0.5



Which of the following exotic options would be very sensitive to the forward skew:

a) Asian
b) Lookback
c) Cliquet
d) Barrier



For very low strikes, such that K/S << 1, we have


a) N(d₂) ≈ 0
b) N(d₂) ≈ 1
c) N(d₂) ≈ ∞ (very large)
d) N(d₂) ≈ 0.5



The magnitude of the convexity adjustment between a variance swap and a volatility swap:

a) Depends on the volatility of the realized volatility but is actually model     independent;
b) is model dependent;
c) both (a) and (b)
d) None of the above;



In Black-Scholes option pricing model, N(d₂) is:


a) is the hedge ration, delta;
b) is the probability of the option finishing in the money;
c) is probability of the option finishing out of the money;
d) is the second derivative of the option price with respect to the strike;

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