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Quantitative Finance · Begrippenlijst

Wat is Accumulator?

Definition 20.7 Derivatives and Volatility · Hoofdstuk 20 — FX Derivatives

An accumulator is the equity or currency analogue in which the client buys (or sells) a fixed quantity at a discounted strike on each fixing while a knock-out barrier has not been touched, and twice the quantity when the price is on the wrong side of the strike.

A zero-cost TARF on the chapter’s pair (client sells the dollar at 7.312, twice the notional above it, target 0.30). Left: the number of fixings before redemption: most end at the first or second. Right: the client’s expected P&L, per million of monthly notional, if the rate moves by a given amount over the first quarter; the fixings of a TARF that fails to redeem are paid at twice the notional. Data: the tutorial.
Figure 20.3. A zero-cost TARF on the chapter’s pair (client sells the dollar at 7.312, twice the notional above it, target 0.30). Left: the number of fixings before redemption: most end at the first or second. Right: the client’s expected P&L, per million of monthly notional, if the rate moves by a given amount over the first quarter; the fixings of a TARF that fails to redeem are paid at twice the notional. Data: the tutorial.

Voorbeelden

Example 20.8 (A TARF on the pair)

The client sells one million dollars at each of twelve monthly fixings at a strike KK: a gain of K−SK-S per dollar when the fixing is below KK, a loss of 2(S−K)2(S-K) when above, and redemption once the gains reach 0.30 per dollar. Under stochastic-local volatility (mixing 0.5) the zero-cost strike is 7.312, against a spot of 7.00 and a one-year forward of 6.861. The client is offered a rate 6.6% better than the forward. The TARF redeems in 98.1% of paths, after 1.73 fixings on average, and 95% of paths end with a gain of at least 126 000 (Figure 20.3, left). The zero value comes from the other 5%. If the rate rises by 10% over the first quarter, the client’s expected loss is 7.12 million per million of monthly notional: 1.01 million in the first quarter and the rest over nine more fixings at twice the notional. A rise of 5% costs 0.99 million, while a rise of up to 2.5% still lets the TARF redeem with the full 0.30 million (Figure 20.3, right).

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