Scenarios
Option written by dealer
Strike \(K/S_0\)
1.05
Time to expiry
30 days
Volatility \(\sigma\)
60%/yr
Drift \(\mu\)
+100%/yr
Net exogenous buying pressure (retail demand, news flow).
Dealer hedging
Dealer's option position: 40% of float. Hedge (% of underlying): \(0.40 \times \Delta_t\).
Price impact \(\lambda\)
1.0
Dealer hedging moves prices by \(\lambda\times\)(hedge flow). So \(\lambda=1\) means dealers move the price by 1% for every 1% of float they buy.
Day 0 of 30
Price path, daily hedging flow, and total dealer hedge
━━ Baseline (no feedback) · ━━ With feedback · ‒ ‒ Strike
Day 0
\(S_t = \) $100.00
\(\Delta_t = \) 0.500
\(H_t = \) 0.0% of float