Pricing Formula for Exotic Options with Assets Exposed to Counterparty Risk

Abstract

This paper gives analytical formulas for lookback and barrier options on underlying assets that are exposed to a counterparty risk. The counterparty risk induces a drop in the asset price, but the asset can still be traded after this default time. A novel technique is developed to valuate the lookback and barrier options by first conditioning on the predefault and the postdefault time and then obtain the unconditional analytic formulas for their prices.

Option Pricing for Path-Dependent Options with Assets Exposed to Multiple Defaults Risk

“…If the default times satisfy situation I, then the dynamic of stock price process takes the form as (11). By Ito's lemma and (11), we can obtain…”

“…Ma et al, in [10], obtain that the explicit valuation of European options with the asset exposed to exogenous counterparty default risk. Yan derives analytical formulas for lookback and barrier options on underlying assets that are subject to an exogenous counterparty risk in [11]. e explicit pricing formulas for European option with asset exposed to multiple defaults risk is given by He [12].…”

“…We use the conditional density approach of default, which is particularly suitable to study what goes on after the default and was adopted by Jiao and Pham [8] for the optimal investment problem, to derive the explicit distribution of the first passage time and then obtain the analytic formulas for valuation of the barrier and lookback options. We also compare the pricing results of the multiple defaults risk model with Merton's [2] default-free option model and Yan's [11] exogenous counterparty default risk option model. e organization of the rest of this paper is as follows.…”

“…It is obvious that the value of up-and-out barrier call option at time 0 under model (1) is the same as the one at time 0 with the stock exposed to counterparty risk (see Yan [11]). (2) If λ 1 � 0 and λ 2 � 0, i.e., there is no any default in model (1), then the risk-neutral price of up-and-out barrier call option at time 0 under this model becomes…”

Explicit Pricing Formulas for European Option with Asset Exposed to Double Defaults Risk

“…Yan derived analytical formulas for lookback and barrier options on underlying assets that are subject to an exogenous counterparty risk (see Yan [9]). However, the derivation of the analytic formula for pricing European call and put options under the double defaults risk model has not been done in the previous literature.…”