SVI 304 · Tier 300 — Advanced — Stochastic & Volatility · 3 credits
Options Structures & Dealer Exposure
Multi-leg payoffs, probability of profit, gamma exposure, the variance risk premium, and the no-arbitrage checks behind the arb scanner.
Prerequisites
Learning Objectives
- Write the payoff of any single option leg as a kinked piecewise-linear function and identify its kink at the strike.
- Derive a position's probability of profit by integrating the risk-neutral density over the region where its payoff exceeds the premium paid.
- Explain why an option dealer's delta-hedging forces them to trade the underlying, and how gamma sets the direction and size of that trade.
- Define the variance risk premium as the gap between the risk-neutral and physical expectation of realized variance, and state its typical sign.
- State the three static no-arbitrage constraints on an option surface — vertical (call) monotonicity and slope bounds, butterfly convexity, and calendar monotonicity in total variance — and explain what trade enforces each.