Basic

The Greeks

An option is not one number. It is a position whose risk comes from several at once: what it is worth now, how fast it moves, and how time decays. The Greeks are the names of those parts.

What you will see

One. A short leg inside a long book is where the curvature lives.

About 1 min of reading

Try It

Compute the parts of one position

1

Write the position

printf 'call 100 60 2\nput 100 40 2\n' > /tmp/book.txt; wc -l < /tmp/book.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
Two legs. A strangle, which is a position with curvature.
2

Sum the linear part

awk '{s+=$1} END {print s}' /tmp/book.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
200. That is the notional, and it is not the risk.
3

Name the part that is not summed

grep -c 'put' /tmp/book.txt

Before you run it, say out loud what it will print. Then open the answer.

What it prints
One. A short leg inside a long book is where the curvature lives.

Data Flow

A position to its parts
1 The position is written as legs
↓
2 Each leg gets its parts
↓
3 The linear parts are summed
↓
4 The curved parts are kept separate
Why this works
Why the Greeks are computed, not looked up

A table is right at one moment and wrong the next. A function is right at every moment you can name.

The trap of summing Greeks

Portfolio delta is a sum, portfolio gamma is not. Adding curvature across positions is the error that makes a book look safe.

Examples

The part that is worth now

Delta is the change in value for a move in the underlying. It is the part that behaves like a stock position.

The part that is not linear

Gamma is the curvature. It is why two positions with the same delta can have very different risk.

The part that decays

Theta is the time cost. It is the only Greek that is a rate, and rates are the ones that compound.

Words this lesson uses

Each one is defined here on this site. Open the entry for the full definition and the other words it points at.

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