Trader's Quiz on Volatility: Quiz # 4
Team Latte
August 10, 2008

Consider an up and out barrier option with annualized volatility of the asset at 25% and a maturity of one year. The monitoring of the barrier is done daily. A trader who is trading this option gets a price from his quant which assumes continuously monitored barrier level. However, the barrier only can be monitored discretely, i.e. on a daily basis. If the trader enters into this trade he would have mis-priced the option approximately by:


(a) 0.65% of the barrier;
(b) 1.26% of the barrier;
(c) 2.15% of the barrier;
(d) 3.45% of the barrier;




A trader is short a lookback call option. He would most likely hedge this short position by:


(a) going long (buy) on two vanilla call;
(b) going long on three vanilla call;
(c) going long on one vanilla call and two vanilla put;
(d) None of the above;




Which of the following statements about Local volatility is TRUE:


(a) Volga measures the convexity due to random volatility;
(b) Vanna measures the convexity due to random volatility;
(c) Vega measures the convexity due to random volatility;
(d) Convexity due to random volatility cannot be measured;




It is generally known to option traders (more or less as rule of thumb) that:

(a) Local volatility varies with the market level about twice as rapidly as the
          implied volatility varies with the strike;
(b) Local volatility varies with the market level about half as rapidly as the
          local volatility varies with the market level about twice as rapidly as the
(c) Local volatility varies with the market level at the same rate as implied
          volatility varies with the strike;
(d) Local volatility varies extremely rapidly with the market level though it has
          no definite relationship with the movement of implied vols with the strike.




A quant is analyzing the market for Napoleon options (Napoleon options are a form of cliquet options). The forward skew is not too steep but the distribution has fat tails (higher volatility of volatility). His most likely choice of volatility model for pricing these options would be:


(a) for out of the money (OTM) strikes;
(b) for in the money (ITM) strikes;
(c) for at the money (ATM) strikes;
(d) nowhere;




In Heston (1993) stochastic volatility model, volatility diffuses as a:


(a) Cox, Ingersoll and Ross (CIR) process:
(b) shorting an index option and going long on a basket of options on the
          individual stocks which comprise the index;
(c) going long on an index option and shorting the underlying index;
(d) shorting the index option and going long on the underlying index;



Which of the following is TRUE about Heston-Nandi volatility model:


(a) Hull-White (1987) model;
(b) SABR model;
(c) BGM model;
(d) HJM model;




A trader is trading put options on Astra Motor Company and believes that there is a very good chance of the company going bankrupt in the near term. The pricing engine that he uses generates option prices using a volatilty surface and local volatilities. He believes that local volatility would under price the out of the money puts. He would most likely:


(a) the change in the dollar value of the options book with respect to one vol
          point move;
(b) the change in the dollar value of the options book with respect to one basis
          point move in the risk free rate;
(c) sensitivity of the options book to the changes in volga;
(d) None of the above;




A quant is setting up his team and implementing models and systems in a bank. The bank is planning to enter the exotic options and structured products market in equities in a big way and would want its traders to run their books. The quant is entrusted with choosing suitable methodologies for implementing various pricing and risk models. His most likely choice for model implementation methodology would be:

(a) Finite difference and lattice methods;
(b) Tree (including, stochastic parameter tree) methods;
(c) Monte Carlo simulation methods;
(d) Closed form methods;



A one touch option is worth two European binary option when:


(a) the log drift is zero;
(b) the log drift is one;
(c) the log drift is infinity;
(d) none of the above;