Autocallable note pricing
The product banks sold by the thousand and hedged badly. A Phoenix pays a fat coupon while the underlying stays above a coupon barrier, redeems early the first time it trades above the autocall level, and hands back the capital loss if it finishes below the protection barrier. The buyer is short a down-and-in put and short a strip of digital coupons.
| Observation | Calls here | Cumulative | Survives |
|---|---|---|---|
| 0.25y | 6.53% | 71.48% | 28.52% |
| 0.50y | 1.90% | 78.88% | 21.12% |
| 0.75y | 0.92% | 82.78% | 17.23% |
| 1.00y | 0.83% | 85.40% | 14.60% |
| 1.25y | 0.65% | 87.55% | 12.45% |
| 1.50y | 0.27% | 88.67% | 11.33% |
| 1.75y | 0.38% | 89.57% | 10.43% |
| 2.00y | 0.22% | 90.37% | 9.63% |
| 2.25y | 0.25% | 90.90% | 9.10% |
| 2.50y | 0.25% | 91.62% | 8.38% |
| 2.75y | 0.22% | 92.00% | 8.00% |
| 3.00y | 0.18% | 92.40% | 7.60% |
An autocallable is short a down-and-in put and short a strip of digital coupons. The issuer is not betting the index falls — it is betting realised volatility stays below the implied volatility it sold, and hedging that with a static option book is where the losses come from.
S_t = S_0 exp[(r−q−½σ²)t + σW_t] · Geometric Brownian motion, one step per observation.
if S_t ≥ K_a: redeem 100 + coupons · Terminates at the first observation above the level.
if S_t ≥ K_c: pay c/f · With memory, missed coupons are recovered later.
100·min(1, S_T/S_0) if S_T < K_p · The down-and-in put that the investor is short.
A clear path from inputs to results.
The product banks sold by the thousand and hedged badly. A Phoenix pays a fat coupon while the underlying stays above a coupon barrier, redeems early the first time it trades above the autocall level, and hands back the capital loss if it finishes below the protection barrier.
How to use
- Set the underlying, volatility and rates.
- Choose the term and how often it is observed.
- Set the autocall, coupon and protection barriers and the coupon rate.
- Read the fair value, the fair coupon and the autocall distribution.
The formula
Reference: Standard Monte Carlo structured-product practice; the payoff convention follows the Phoenix autocallable described in Bouzoubaa & Osseiran, Exotic Options and Hybrids.
Worked example
A three-year Phoenix at 8% with a 60% protection barrier
- Spot 100, 20% volatility, 3% rate.
- Monthly observations, autocall at 100%, coupon barrier 70%, protection 60%.
- 8% coupon with memory, 4,000 paths.
- 1
Each path is simulated monthly under geometric Brownian motion.
- 2
The first observation above 100% redeems the note at par plus accrued coupons.
- 3
With a 20% volatility, roughly half the paths call at the first observation, so 92.4% call eventually and the expected life is only 0.51 years.
- 4
The 1.8% of paths that finish below 60% lose an average of 48.7% of capital.
- 5
Discounting every payoff gives a fair value of 101.02 against a 5.57% fair coupon.
101.02 fair value · 5.57% fair coupon · 92.4% called · 1.8% loss.
Interpreting the result
The note is worth more than par at an 8% coupon, which means the quoted coupon is generous relative to the risk — unusual, and a sign that the issuer expects to hedge the embedded short put more cheaply than the model assumes. The expected life of half a year against a three-year term is the other thing to notice: most of the return comes from being called early.
Assumptions & limitations
- Geometric Brownian motion with constant volatility.
- Continuous observation of the barriers at the stated dates only.
- No dividends beyond the stated yield, no funding spread, no credit risk.
- The Monte Carlo is seeded, so the same inputs give the same price.
Frequently asked questions
Why is the expected life so short?
Because the autocall level is at the money: with any volatility, the underlying crosses it early. A note with a 110% autocall level would have a much longer expected life.
Is the fair coupon the same as the quoted coupon?
No. The fair coupon prices the note at par; the quoted coupon is what the distributor offers after their fee and the issuer's margin.
What does coupon memory do?
It banks coupons missed at a breached barrier and pays them at the next observation that clears it. Without memory, a missed coupon is simply lost.
What risk is the issuer short?
A short down-and-in put and a short strip of digitals, hedged with a static option book. The residual risk is the correlation between spot and volatility, which the model cannot see.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.