medium · Quantitative Finance stochastic
The BSM derivation assumes 'no arbitrage'. If the hedged portfolio Π earned more than the risk-free rate r, what specific action would an arbitrageur take?
- Borrow cash at the risk-free rate to buy the portfolio Π, locking in a riskless profit.
- Sell the portfolio Π and invest all the proceeds into the stock S right away.
- Buy stock S and sell the call V, but keep the hedge ratio Δ fixed and unadjusted throughout.
- Wait for the implied volatility to decrease before entering into any arbitrage trade whatsoever.
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