Correlation & Dispersion Pricer
Price the two ways a desk trades correlation — a direct correlation swap, and a variance-swap dispersion trade — with implied vs realized correlation and the net hedge P&L, instantly.
Educational tool, not investment advice. The dispersion P&L uses the standard vega-notional variance-swap approximation on a flat vol per name; it ignores var-swap caps, the convexity/skew adjustment and financing. Correlation swaps are illiquid and quoted wide.
This free correlation and dispersion tool prices the two trades a structured-products desk uses to manage its short-correlation exposure. A book of autocalls and worst-of options is long worst-of puts, which lose value as correlation rises — so the desk must buy correlation back. There are two ways to do it, and the tool covers both.
The direct way: a correlation swap
A correlation swap pays Notional × (realized correlation − strike). It is the cleanest expression of a correlation view — linear, crossing zero at the strike — but the instrument is OTC, illiquid and quoted wide, and the market maker cannot replicate it statically.
The liquid way: dispersion via variance swaps
Index variance is approximately correlation times the squared weighted-average single-name vol, so going long index variance and short the single-name variances is a long-correlation, short-dispersion trade — the hedge the book needs. The tool values each leg as a variance swap in vega notional, computes the implied and realized correlation (both the simple dirty measure and the clean one that removes the idiosyncratic variance), and nets the legs into a single P&L. For the volatility building blocks, see the Variance Swaps pricer and Volatility Models; for the products that create the short-correlation exposure, see Structured Products.
What to read off it
The net dispersion P&L turns positive when realized correlation beats implied — exactly when the short-correlation book is losing, so the hedge offsets it. The honest caveats: basis risk between index and single-name vols, caps on single-name variance swaps, and correlation running to 1 in a crash, when the hedge costs the most at the worst possible moment.
Frequently asked questions
Why is a structured-products desk short correlation?
A book of autocalls and worst-of options leaves the dealer long worst-of puts, which lose value when correlation rises (a higher correlation makes the worst performer less extreme). So the book is structurally short correlation and must buy correlation back to hedge — either directly with a correlation swap, or indirectly by selling dispersion.
What is the correlation swap payoff?
A correlation swap pays Notional × (realized correlation − strike), where the strike is the implied correlation agreed at inception and the notional is quoted per 1.00 of correlation. The payoff is linear in realized correlation and crosses zero at the strike. It is the direct expression of a correlation view, but the instrument is OTC, illiquid and quoted wide.
How does the dispersion trade express a correlation view?
Index variance is roughly correlation times the square of the weighted average single-name vol: σ²_index ≈ ρ·(Σ wᵢσᵢ)². Going long index variance and short the single-name variances is therefore long correlation — a short-dispersion position, which is exactly the hedge a short-correlation book needs. The tool expresses both legs as variance swaps in vega notional.
What is the difference between dirty and clean implied correlation?
Dirty correlation is σ²_index / (Σ wᵢσᵢ)² — simple, but it still carries the idiosyncratic single-stock variance Σ wᵢ²σᵢ². Clean correlation strips that term out, (σ²_index − Σ wᵢ²σᵢ²) / ((Σ wᵢσᵢ)² − Σ wᵢ²σᵢ²), giving the correlation implied by the systematic part alone. The tool shows both, for implied and realized vols.
When does the dispersion hedge make money?
The net P&L is positive when realized correlation exceeds implied — precisely when the short-correlation structured book is losing, so the hedge offsets it. The catches: basis risk between index and single-name vols, caps on single-name variance swaps, and correlation running to 1 in a crash, when the hedge is most expensive exactly when you need it.