Tim Olson
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54 lines
3.6 KiB
Markdown
54 lines
3.6 KiB
Markdown
---
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description: "Volatility skew risk reversal strategy buys an OTM call and sells an OTM put to exploit the empirical skew where put implied volatility exceeds call implied volatility, capturing a directional upside bias at reduced net premium cost."
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tags: [volatility, skew, risk-reversal, options, put, call]
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---
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# Volatility Skew — Long Risk Reversal
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**Section**: 7.5 | **Asset Class**: Volatility | **Type**: Volatility Skew / Directional
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## Overview
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OTM put options are empirically priced with higher implied volatility than OTM call options at the same distance from the current spot price. This volatility skew (puts more expensive than calls) reflects market demand for downside protection. The long risk reversal — buy an OTM call, sell an OTM put — captures this skew by selling the expensive put and buying the cheaper call, resulting in a net credit or reduced debit. However, the strategy has a directional component: it loses money if the underlying falls below the put strike.
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## Construction / Mechanics
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**Volatility skew setup**: with underlying S_0 = K (at-the-money), and OTM options at distance κ > 0:
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- OTM put: strike K_put = K - κ; implied vol σ_put (higher)
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- OTM call: strike K_call = K + κ; implied vol σ_call (lower)
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- Skew: σ_put > σ_call (puts priced richer than calls at the same moneyness)
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**Long risk reversal position**:
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- **Buy** OTM call (strike K + κ): pays premium C_call
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- **Sell** OTM put (strike K - κ): receives premium C_put > C_call
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- Net premium received: C = C_put - C_call > 0 (net credit due to the skew)
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Reference: see Section 2.12 of the book for the basic risk reversal option strategy.
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## Payoff / Return Profile
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- **If S_T > K + κ** (underlying rallies above call strike): call expires ITM; gain = S_T - (K+κ) + C
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- **If K - κ < S_T < K + κ** (underlying stays between strikes): both options expire worthless; gain = C (the net premium received)
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- **If S_T < K_put** (underlying falls below put strike): put expires ITM; loss = K_put - S_T - C; maximum loss when S_T → 0 is K_put - C
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- Break-even on the downside: S_T = K_put - C
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The strategy profits when the underlying rises or stays stable, and loses when the underlying falls.
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## Key Parameters / Signals
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- K_put = K - κ: put strike (sold)
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- K_call = K + κ: call strike (bought)
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- κ: distance from ATM (moneyness)
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- C = C_put - C_call: net premium received (positive due to skew)
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- σ_put - σ_call: implied volatility skew — the size of the mispricing being exploited
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- K_put - C: downside break-even level
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## Variations
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- **Short risk reversal**: sell OTM call, buy OTM put — a bearish, downside bet; profits if underlying falls below the put strike.
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- **Skew trade without directional bias**: combine the risk reversal with a Delta hedge to isolate the pure skew component.
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- **Different distances**: use asymmetric κ_put ≠ κ_call to fine-tune the net premium and directional exposure.
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## Notes
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- This is a directional strategy: it loses money if the price drops below K_put - C; the skew-capture is bundled with an implicit bullish bet.
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- The strategy profits most clearly in a stable or rallying market with sustained volatility skew.
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- The skew is typically larger for equity indexes than individual stocks (reflecting systematic put-buying for portfolio hedging).
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- To isolate the pure skew trade (without directional exposure), the position should be Delta-hedged dynamically, which introduces transaction costs and complexity.
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- Risk reversals are commonly used by FX traders where the skew direction can differ from equities (e.g., EURUSD calls can be more expensive than puts in certain regimes).
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