Exotic components

Exotic products are not quoted on the market: their price is only an estimate given by the model. An exotic component is useful to represent a specific risk driver of the product.

Termsheet (core components)

2Y USD 14% p.a. Autocallable Multi Reverse Convertible (55% European) on Microsoft, Oracle

• Barrier = 55%, European
• Strike = 65%
• Autocall level = 100%

Payoff

Below the barrier, the investor still receives the coupons (28). The put he shorted is exercised: he must buy $100/65$ shares of the worst performer at 65 (% of initial) while these are only worth $W$, i.e. a loss of $\frac{100}{65}(65 - W)$. Hence P&L $= 28 - \frac{100}{65}(65 - W) = 28 + 100 \cdot W/65 - 100$.

Investor exposure

• Long zero-coupon bond -> vanilla
• Short worst-of down-and-in put -> exotic
• Long coupons -> vanilla (replicable with Treasury STRIPS, i.e. a strip of zero-coupon Treasury bonds)
• Short autocall -> exotic

Calibration step

Note: at low spot, the surface has holes. These come from our SVI fit/interpolation that is too simplistic (missing a no-arbitrage constraint).

Pricing steps

1/ Load the inputs

2/ Simulate correlated paths under local vol

• Use Cholesky to generate correlated returns
• Build the grid -> list of uniform (all trading dates + insertion of important dates like observation/calling dates)
• Simulate the price at each step using the local vol SDE

3/ Check the simulations

• Check martingale: $\mathbb{E}[S(t)]$ (simulation) should be equal to the $F(t)$ (deduced from Call-put parity)

4/ Compute the worst-of

• Observed at valuation dates

5/ Build the cashflows

• Cash flows are mostly principal repayment (if called) + coupon
• Cash flows are paid at payment dates

6/ Discount and average

• Use of the risk-free rate

7/ Describe the redemption profile

• Autocall probabilities: proportion of paths that triggers an autocall
• Barrier probabilities

-> computed in order to understand better the price

8/ Solve for the fair coupon at inception

• Based on the redemption price (price decomposition)

9/ Run sensitivities

• Stress test some parameters like correlation or funding spread