Defining common or particular payoff functions for Express Certificates
payoffExpressClassic(i, n, S, m, K)
payoffExpressML0AN5(i, n, S, m, K, B, S0)
payoffExpressCappedBonusType1(i, n, S, m, K, B)
payoffExpressBonusType1(i, n, S, m, K, B)The redemption date (\(i=1,...,n\))
The number of valuation dates
A vector of length n for the prices at the valuation dates, i.e. \(S(t_1),...,S(t_n)\)
A vector of length n for the running minimum at the valuation dates, i.e. \(m(t_1),...,m(t_n)\)
A vector of fixed cash rebates at early redemption times
A barrier level to be monitored
underlying start price
returns the certificate payoff (Not discounted payoff!) for the given inputs at time i
Payoff structure of express certificates can be either path independent or path dependent,
while monitoring a barrier B.
Path independent payoffs:
The function payoffExpressClassic implements the following payoff at \(t_i\):
$$p(t_i) = K(t_i) \quad \textrm{for} \quad i < n, \quad \textrm{else} \quad S(t_n)$$
Path dependent payoffs:
The function payoffExpressCappedBonusType1 implements the following payoff:
| \(p(t_i) =\) | \(K(t_i)\) | \(\textrm{ for } \quad i < n\) |
| \(S(t_n)\) | \(\textrm{ for } i = n \textrm{ and } m(t_n) \le B\) |
In case the barrier has not been hit during the lifetime, a fixed bonus payment \(K(t_n)\) is payed and the payoff is therefore capped.
The function payoffExpressBonusType1 implements the following payoff:
| \(p(t_i)\) | \(K(t_i)\) | \(\textrm{ for } \quad i < n\) |
| \(S(t_n)\) | \(\textrm{ for } i = n \textrm{ and } m(t_n) \le B\) |
Unlike in the payoffExpressCappedBonusType1,
this payoff is not capped for the case (\(S(t_n) > K(t_n)\))
The function payoffExpressML0AN5 is an example of an quite complicated payoff including
path dependence and coupon payments. See also the certificate prospectus ../inst/doc/ML0AN5.pdf.
See also the generic pricing function SimulateGenericExpressCertificate