# Consider a typical term in g(x,t) where can be either 2n(u ) or 2 +

## Question:

Consider a typical term in g(x,t)

where ξ can be either 2n(u − ℓ) or 2ℓ + 2n(u − ℓ). Show that the above term can be rewritten as

Hence, show that

Use the above result to derive the price formula of the European double knockout call option c^{o}_{LU} [see Sect. 4.1.3].

We generalize the barriers to become exponential functions in time. Suppose the upper and lower barriers are set to be Ue^{δ1t }and Le^{δ2t} ,t ∈ [0,T ]. Here, δ_{1} and δ_{2} are constant parameters and the barriers do not intersect over [0,T ]. Show that the price formula of the European double knock-out call option can be expressed as (Kunitomo and Ikeda, 1992)

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