Quantile Hedging for Defaultable Securities in an Incomplete Market - Proceedings ASTIN/AFIR 1999 - Tokyo, Japan

In this paper, we aim at 1. giving formulas of prices and replicating-strategies of defaultable securities(e.g., bonds, swaps, derivatives) in incomplete market, and 2. giving “solvable” examples of quantile hedging strategies in incomplete market. Considering an incomplete market that consists of tradable assets and an unhedgeable defaultable security, whose non-predictable default time has stochastic intensity correlated with the tradable assets-priceprocess, we treat the problem of pricing and hedging of the defaultable security on it. We employ the quantile hedging strategy (cf., [F-L]) to replicate “the cumulative dividend process” of the defaultable ‘security by an admissible strategy between the tradable assets. The strategy that maximize the success probability of hedge under the given initial capital and the strategy that minimize the initial capital under the given success probability of hedge are calculated explicitly.