Option Portfolio
Combine calls, puts, shares and futures on one underlying, each option with its own strike, expiry and volatility, and read the book's value and net Greeks.
Learning focus: a book's Greeks are the signed sums of its positions' Greeks, so written options flip the sign of their delta, gamma and vega, and the delta–gamma–vega estimate of a move is only as good as the move is small.
The move happens at once, so no time passes. The book is repriced in full and compared with the Greeks' estimate.
Quantity counts options each on one unit of the underlying (for 100-share contracts enter 100 × contracts), shares, or futures units. Written options and short positions count with a minus sign. A blank volatility uses the default. A futures position is entered at the futures price agreed, F₀, and is worth F − F₀ with F = S e^((r − q)T).
| Position | Value per unit | Value | Delta | Gamma | Vega (1%) | Theta (day) | Rho (1%) |
|---|---|---|---|---|---|---|---|
| 1. written 1,000 calls K 100.00, 0.50 yrs | 6.8887 | −6,888.73 | −597.73 | −27.3587 | −273.59 | 22.24 | −264.42 |
| 2. long 500 puts K 95.00, 0.25 yrs | 1.5343 | 767.13 | −122.87 | 15.7440 | 78.72 | −6.84 | −32.64 |
| 3. long 400 underlying | 100.0000 | 40,000.00 | 400.00 | 0.0000 | 0.00 | 0.00 | 0.00 |
| Book | 33,878.40 | −320.61 | −11.6147 | −194.87 | 15.40 | −297.06 |
Each figure is for the whole position, with its sign: a written call has negative delta, gamma and vega. The book row is the sum of the column.
For small moves the delta–gamma–vega estimate is close to the full revaluation; the gap grows with the size of the move, because gamma and vega themselves change as the spot and volatility move.
The solid line is the book's Black–Scholes–Merton value today; the dashed line is its value on the nearest expiry date, when the shortest-dated options are worth their intrinsic value and longer-dated ones still carry time value.