TARN on REVERSE CMS

Analysis by PRICING PARTNERS

Pricing Partners, independent valuation expert

Pricing Partners is a service provider of independent valuation and international software developer of derivatives pricing analytics.

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Product description:
This product pays a coupon whose performance is directly linked to the 10Y swap rate using the coupon on reverse CMS. More specifically, the coupon is given by the formula 12% - 2* CMS10Y floored at 2% and capped at 8%, or Min[8% ; Max(2% ; 12% - 2* CMS10Y)].

The coupons are paid until the sum of coupon payments reach 30%. As soon as the sum of coupon payments exceeds 30% on a payment date, the last coupon is adjusted so that the sum makes exactly 30%. The structure is automatically cancelled, and the nominal is repaid at par. In addition, if at maturity, the sum of coupon payments did not reach 30%, an additional coupon is paid, in order to reach 30%.

Product Features :

Cash Flow example:
In this simple example, we provide the value of the underlying swap. This underlying swap receives the coupon of TARN and pays the floating leg (in our case, the 6-month Euribor) until the sum of coupon payments reach 30%.

The cash flow table

In this scenario, the value of the swap is near zero, indicating that the note should be issued to 100.

Pricing & Risks :
Ignoring the plight RNA, this product would be a simple reverse CMS capped and floored. A proper pricing of coupon depends on good modeling CMS options (which can be successfully replicated by a combination of swaptions). The condition RNA adds a risk of smile, as the strike is implicit Fortent RNA-dependent stochastic coupons paid successively. The product price is by using a model markov fonctional "which allows a proper consideration of the smile.

It should be noted that the TARN condition makes the operation look more attractive because the operation is canceled when the sum of paid coupon reaches 30%.

The study of the Greek shows that the product is very sensitive to the moves of interest yield curve. The volatility risk, measured by the Vega is not negligible, since the movements of the volatility surface have impacts on both coupons of reverse CMS and the TARN condition.

Strategy returns table :

In this example, the probability of reverse CMS returns to be between 2.5% and 5% is 75%.
The probability to be between 5% et 7.5% is 15%, and the one to be below 2.5% is lower than 10%.

Performance analysis: