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Quantitative Finance · Begrippenlijst

Wat is Box spread?

Definition 1.4 Derivatives and Volatility · Hoofdstuk 1 — No Arbitrage and the Fundamental Theorems

A box spread with strikes K1<K2K_1<K_2 and one expiry is a long call and a short put at K1K_1 together with a short call and a long put at K2K_2. At expiry it pays K2−K1K_2-K_1 in every state, so its price is P(0,T)(K2−K1)P(0,T)(K_2-K_1) and it is a zero-coupon bond.

The four legs of a 5 000–6 000 box spread at expiry. Each leg has its kink at its strike; the calls’ kinks and the puts’ kinks cancel, and the sum is the flat line at 1 000 points. Data: the chapter’s code.
Figure 1.1. The four legs of a 5 000–6 000 box spread at expiry. Each leg has its kink at its strike; the calls’ kinks and the puts’ kinks cancel, and the sum is the flat line at 1 000 points. Data: the chapter’s code.

Voorbeelden

Example 1.5 (Reading the rate off a box)

The one-year 5 000–6 000 box of the opening trades at 958.90 points. Its continuously compounded rate is −ln⁡(958.90/1000)=4.20%-\ln(958.90/1000)=4.20\%. A lender who buys it pays USD 95 890 and receives USD 100 000 in a year (the multiplier is USD 100 per point); a borrower sells it.

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