Two Asset Cash Or Nothing Option

Two asset cash-or-nothing options have four types:
[1] Cash-or-nothing call
   Pays out cash K if S1 > X1 and S2 > X2 at expiry.

[2] Cash-or-nothing put
   Pays out cash K if S1 < X1 and S2 < X2 at expiry.

[3] Cash-or-nothing up-down
   Pays out cash K if S1 > X1 and S2 < X2 at expiry.

[4] Cash-or-nothing down-up
   Pays out cash K if S1 < X1 and S2 > X2 at expiry.


Below a table with call and put prices for given parameters.
  • Input Parameters
  • TypeFlag
  • S1 - asset 1
  • S2 - asset 2
  • X1 - strike 1
  • X2 - strike 2
  • K - cash
  • T - time to maturity in fraction of a year
  • r - risk free interest rate
  • b1 - carry asset 1
  • b2 - carry asset 2
  • v1 - volatility asset 1
  • v2 - volatility asset 2
  • rho - correlation
  • Parameter Values
  • TypeFlag
  • 100
  • 100
  • 110
  • 90
  • 10
  • 0.5
  • 0.1
  • 0.05
  • 0.06
  • 0.20
  • 0.25
  • 0.50
  • Type Prices
  • Type 1: 2.4987
  • Type 2: 2.1567
  • Type 3: 0.2128
  • Type 4: 4.6440