IAI Actuarial Core Principles · Economic Modelling · Stochastic models for security prices
Under Black-Scholes, a European call has delta 0.60 and the share price is Rs 200. A dealer writes 1,000 calls (each on one share) and delta-hedges using the share. Immediately after the share price rises by Rs 1, and ignoring gamma, what is the approximate net change in the value of the dealer's hedged portfolio (short calls plus held shares)?
The net change is approximately zero. The dealer holds 600 shares, gaining about Rs 600, while the 1,000 short calls lose about Rs 600 for a Rs 1 rise, so the delta-hedged position is neutral to first order.
- ARs 0 approximatelyCorrect
- BRs +400
- CRs -600
- DRs +600
- Rs -400
Explanation
The dealer holds 600 shares (delta 0.6 x 1,000). Shares gain 600; the short calls lose about 1,000 x 0.60 = 600. The net change is about zero to first order, which is the purpose of delta hedging. Rs 400 comes from using 1 minus delta wrongly.
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