FE Problem Set #15
November 1, 2006
Note : You will need a PC or Laptop computer and Excel spreadsheet to work on all or most of the following problems .
The structuring desk of a European bank is contemplating a 5 year equity linked note on a basket of four European telecommunications stocks as the underlying and a final payoff at maturity as:
One of the issues that the structurers are grappling with is: how much should be the maximum coupon in the above payoff? This needs to be specified in the term sheet. The second issue concerns the impact of volatility of the underlying stocks on the structure and whether a stochastic volatility or local volatility model needs to be applied to correct pricing.
- Decompose (reverse engineer) the above structure into constituent exotic options that are embedded in it;
- Suggest way of estimating, if possible, the fair value of the coupon in the above structure;
- Suggest a suitable volatility model for pricing the above structure.
- As far as the return of the baskets are concerned will there be any skew dependence? Explain.
- Assuming a risk free interest rate of 4%, constant volatility of all the underlying stocks of 15% and a constant correlation of 0.5 between all the pairs of stocks in the basket estimate a value for the note. Assume a notional of $100 and the current spot price of all the stocks as 100. You may use any method to value the note.
- Comment on the structure.
The risk neutral probability density function of a stock (or an asset, such as a currency pair or a commodity) is given by:
In stating the above equation it is assumed that an infinite strip of European call options are available on the underlying stock or the asset and is the strike price of a European call option, on the stock that matures at time .
Estimate the risk neutral probability density function of the underlying stock.
- How is the local and implied volatility affected in Merton's "jump-to-ruin" model? Is there a closed form solution to estimate the local volatility when we take into account the jump?
- What is an SABR volatility model and what is the main feature, or one of the chief characteristics, of SABR model?
- A risk manager is stress testing the correlation matrix of a portfolio of assets for market risk estimation. What major problem will he encounter in doing so?
- What is a Power Reverse Dual Currency (PRDC) Swap?
You are a fund manager and you wish to invest $1 million in a risky asset, say a stock. However, you do not wish to lose more than $100,000 on this investment in a year's time. The risk free rate of interest on government bonds is currently at 5%. Your analyst, a very good one, tells you that the stock can either go up by 30% or down by 15% in a year's time.
- Set up the basic portfolio insurance problem with regard to the above investment;
- What is the cost of the synthetic put option that you will construct using the above strategy.
You are a credit structurer and an investor, a big client of yours, approaches you with the objective of buying credit risk insurance on the Republic of Kryvenia , whose sovereign bonds are trading at 750 basis points above the US Treasury. Let us say that Kryvenia is in Europe and the current one year Euribor is trading at 5% same as the one year USD Libor. Further, since he expects a sizeable volatility in the Euribor rate he wants to pay the premium annually on the protection (insurance) if the 6 month Euribor stays within a specified range every year. It is estimated by him that Euribor could vary from 3.5% to 7% in the next five years.
Assume that the current Euribor yield volatility is 15% per annum and it has a mean reversion speed of 0.05 and a long term rate of 10%.
- Create a structure for the investor and what kind of a structure is it.
- What are the major considerations in pricing this structure;
- Do you have all the parameters to price this structure? If yes, then price this structure assuming a notional of our own. If not, then make suitable assumptions and price this structure.
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