calcRedemptionProbabilities: Redemption Probabilities for Express Certificates

In fExpressCertificates: fExpressCertificates - Structured Products Valuation for ExpressCertificates/Autocallables

Description

Calculates the stop probabilities/early redemption probabilities for express certificates using the multivariate normal distribution or determines stop probabilities with Monte Carlo simulation.

Usage

calcRedemptionProbabilities(S, X, T, r, r_d, sigma)
simRedemptionProbabilities(S, X, T, r, r_d, sigma, mc.steps=1000, mc.loops=20)

Arguments

S	the asset price, a numeric value
X	a vector of early exercise prices ("Bewertungsgrenzen"), vector of length (n-1)
T	a numeric vector of evaluation times measured in years ("Bewertungstage"): T = (t_1,...,t_n)', vector of length n
r	the annualized rate of interest, a numeric value; e.g. 0.25 means 25% pa.
r_d	the annualized dividend yield, a numeric value; e.g. 0.25 means 25% pa.
sigma	the annualized volatility of the underlying security, a numeric value; e.g. 0.3 means 30% volatility pa.
mc.steps	Monte Carlo steps in one path
mc.loops	Monte Carlo loops (iterations)

Details

Calculates the stop probabilities/early redemption probabilities for Express Certificates at valuation dates (t_1,...,t_n)' using the multivariate normal distribution of log returns of a Geometric Brownian Motion. The redemption probability p(t_i) at t_i < t_n is

P(S[i] >= X[i], S[j] < X[j] for all j < i)

i.e.

p(t_i) = P(S[i] >= X[i], S[1] <= X[1],...,S[i-1] <= X[i-1])

for i=1,...,(n-1) and

p(t_n) = P(S[1]<=X[1],...,S[n-1]<=X[n-1])

for i=n.

Value

a vector of length n with the redemption probabilities at valuation dates (t_1,...,t_n)'.

Author(s)

Stefan Wilhelm [e-mail]

References

Wilhelm, S. (2009). The Pricing of Derivatives when Underlying Paths Are Truncated: The Case of Express Certificates in Germany. Available at SSRN: http://ssrn.com/abstract=1409322

Examples

# Monte Carlo simulation of redemption probabilities 
# p(t_i) = P(S(t_i)>=X(t_i),\forall_{j<i} S(t_j)<X(t_j))
mc.loops <- 5000
probs <- simRedemptionProbabilities(S=100, X=c(100,100,100), T=c(1,2,3,4), 
  r=0.045, r_d=0, sigma=0.3, mc.steps=3000, mc.loops=5000)
table(probs$stops)/mc.loops

# Analytic calculation of redemption probabilities
probs2 <- calcRedemptionProbabilities(S=100, X=c(100,100,100), T=c(1,2,3,4), 
  r=0.045, r_d=0, sigma=0.3)
probs2

fExpressCertificates documentation built on May 2, 2019, 4:48 p.m.