Risk Latte - FE Problem Set #17

FE Problem Set #17

Team Latte
May 10, 2009

Note:The following questions were part of the Mid Term Examination of Risk Latte's Certificate in Financial Engineering (CFE) Course in Hong Kong.

Problem #1

If the price of a one year at the money (ATM) call option is 6%, then assuming zero interest rates and no term structure of volatility calculate the approximate, "back of the envelope", price of a six month at the money (ATM) call option on the same asset.

Problem #2

A binary (digital) call option can be valued as a call spread in the limit. The price of a binary, using continuous time calculus, can be expressed as:

For a particular asset the ATM volatility is 25% and the volatility skew (change of volatility across strike price) is 3% per 10% change in strike. If the trader does not take into account the skew then by how much (in percentage terms) will he mis-price a one year binary call option?

Problem #3

For an asset currently trading at 100, with risk free rate at 4%, the following prices of Call and Put options with six month maturity are given:

Strike 91 91.5 94.5 96.5 100 102.5 105 106.5 110
Call 13.62 13.29 11.06 9.78 6.57 4.52 2.35 2.45 3.1
Put 1.05 1.20 1.85 2.5 2.65 3.00 3.23 4.77 8.79

Using the above, what would be a trader's price for a 105 Knock-Out call option with the barrier at 98, i.e. KO(105/98). This is a Down and Out Call Option.

Problem #4

Value the following five year equity linked note (ELN) on Hang Seng Index using both (i) Monte Carlo Simulation and (ii) the Closed form (Black-Scholes) model:

Use a participation rate (alpha) of 65%. Assume a notional of $100 for the note, risk free rate 4%, dividend yield of 3%, floor coupon at 5%, volatility of the Hang Seng index of 20% and the spot price of the index, of 15,000.

Problem #5

If the underlying, , is the Nikkei225 index then value the following one year ELN using both Monte Carlo simulation technique and Closed Form (Black-Scholes) model:

Assume a volatility of 18% and a drift of 1%. Both the Monte Carlo price and the closed form price of the note should converge.


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