Write the initial value of asset ii as Si(0)S_i(0), its value at maturity as Si(T)S_i(T), and the strike as a fraction KK of the initial values. The payoff of the call at maturity is max⁡(min⁡iSi(T)/Si(0)−K, 0)\max\bigl(\min_i S_i(T)/S_i(0) - K,\ 0\bigr)1. It is set by the asset that rose the least2.

Consider a hypothetical example in which a worst-of call with a strike of 100 yen is written on assets 1 and 2, both currently at 100 yen. If asset 1 is at 130 yen and asset 2 is at 70 yen at maturity, the lowest value is 70 yen, so the payoff is 0 yen. If asset 1 is at 130 yen and asset 2 is at 120 yen, the lowest value is 120 yen and the payoff is 20 yen.

At the same strike, the payoff of a worst-of call is never above that of any single-asset call. The payoff of a worst-of put is never below that of any single-asset put.

Notes

  1. Maxime Malgrat, "Pricing of a “worst of” option using a Copula method" (Master of Science Thesis, 2013), chapter 1, section D, "Worst Of options" (PDF page 20). ↩

  2. The Options Industry Council, "Analysis on Structured Products and Listed Equity Options in Europe (Part 1)" (SRP, 2015), the entry "Worst-of option" in the Glossary of Terms (PDF page 54). ↩