Risk Latte - Index Call with FX Barrier
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 Quanto Equity Note Team Latte Apr 11, 2005 We have recently advised one of our clients on the following product. The product is a 5-year equity linked note but with a quanto payoff and is designed for the investor who is bearish on the Japanese equity market. This product is designed for the US Dollar based investor. This equity note is indexed to the inverse of Nikkei 225 index (actually, futures on the index) but the pay off on the note is in US Dollars. The payoff of the note at maturity is: Where, Payoff = Payoff of the Note in USD N = 100 (per unit) S = Nikkei 225 futures in Yen Normally, there will be a participation rate attached to the above payoff formula, but we have deliberately omitted it. Also, the formula appears much simpler without a participation rate. The salient features of the above note are: Though the note is indexed to (the inverse) of Nikkei225 index, which is denominated in Yen, the payoff of the note is in USD; this makes the note a quanto note. The payoff of the note is indexed to the inverse of the Nikkei225 index (futures) which means that if the Nikkei225 index goes down below the level of 12,000 (initial level) the note increases in value and vice versa; therefore an investor who believes that the Japanese stock index will be much lower than 12,000 in five years time stands to make good return from the note. The note has a flaw, i.e. the worst case payoff on the note is 100, or in other words the capital invested in the note. Because it is a correlation product the note's payoff is dependent on the volatility of the Nikkei225 futures, USD/JPY exchange rate and the correlation between the Nikkei futures and USD/JPY FX rate. Pricing the Note: A very simple way to price the note is by using Monte Carlo simulation method. We used the following parameters to calculate the back of the envelope price of the note using MC simulation - volatility of Nikkei index (futures) at 13.52%, volatility of Dollar-Yen at 11% and the correlation between Nikkei and Dollar-Yen at 0.67 and a risk free rate (discount rate) of 2%. The choice of the above parameters came from our client). Using these variables and 10,000 simulation runs we calculated the value of the note as 106.20. Correlation between Nikkei and Dollar-Yen plays an important role in the pricing of the note. For example, using the above parameters, the price of the note increases from 105.45 to 107.69 as the correlation drops from 1.00 to -1.00 (minus one). The IRR (internal rate of return) of the note is a whopping 19.11%. Therefore, this is a very attractive note for any investor who has a bearish view on the market. Note that a higher volatility value for the Nikkei would tend to increase the attractiveness of the note and increase the price of the note. This is because of the inverse (empirical) relationship between volatility and the asset. Detailed Pricing: Later we have refined the pricing (using the same MC Simulation method) as: We used a GARCH method to estimate the terminal volatility and correlation (at the end of 5 years); We also used term structure of volatility - for both Nikkei and Dollar-Yen - to calibrate the model; Of course, a participation rate was included in the payoff formula (the final price was calculated both using a participation rate as well as without it); Three different discount rates were used to benchmark the model; We perform 200,000 simulation runs to calculate the Monte Carlo value. The above modifications to the pricing model make the price more accurate and robust. Any comments and queries can be sent through our web-based form. More on Quantitative Finance >>
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