Question
The opening price of Stock DEF is 100. It just paid out its annual dividend. Its constant, annualized volatility is 50% (we are in a
The opening price of Stock DEF is 100. It just paid out its annual dividend. Its constant, annualized volatility is 50% (we are in a leap year, with 366 days).
The proportional interest rate prevailing in the monetary market (to which you have access as a lender or borrower) is 2.4% (annualized).
This market uses the convention Exact/360. A call on DEF, struck at 95 with duration 60 days, has the following characteristics:
Price = 10.83. Delta = 0.6462. Gamma = 0.0184. Theta = -0.0663.
You have an initial wealth of zero. You build a delta-neutral portfolio comprising, in particular, 1 000 calls sold short. Compute (then carefully check) the change in DEFs closing price (at the end of the trading day) such that your P&L is (up to a very small rounding error) nil.
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