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:

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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