1. The Valuation of Options Subject to Default Risk Shen-Yuan Chen Department of Finance Ming Chuan University

2. Vulnerable OptionShen-Yuan Chen2 Introduction Exchange-listed Options v.s. Unlisted (OTC) Options →Default Risk of the Issuer → Vulnerable option

3. Vulnerable OptionShen-Yuan Chen3 Purpose Extend Klein (1996) vulnerable option pricing model Derive a path-dependent valuation model for vulnerable option

4. Vulnerable OptionShen-Yuan Chen4

5. Vulnerable OptionShen-Yuan Chen5 Klein (1996) Model

6. Vulnerable OptionShen-Yuan Chen6 Path-Independent vs Path-Dependent Vulnerable Options

7. Vulnerable OptionShen-Yuan Chen7 Path-Dependent Vulnerable Options Valuation Model

8. Vulnerable OptionShen-Yuan Chen8 Comparison of Alternative Pricing Models Path-Dependent Vulnerable Option Klein(1996) Black & Scholes (1973) →Tables 1 : Base Case →Tables 2 : V = 10 →Tables 3 : V = 8

9. Vulnerable OptionShen-Yuan Chen9

10. Vulnerable OptionShen-Yuan Chen10

11. Vulnerable OptionShen-Yuan Chen11

12. Vulnerable OptionShen-Yuan Chen12 Sensitivity Analysis → Figure 1 : Counterparty’s asset value → Figure 2 : Volatility of counterparty’s asset value → Figure 3 : Coefficient of correlation → Figures 4 - 7

13. Vulnerable OptionShen-Yuan Chen13

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19. Vulnerable OptionShen-Yuan Chen19 Conclusions Klein (1996) overestimates vulnerable option value Counterparty’s asset value ↑→ PDVO ↑ Volatility of counterparty’s asset ↑ → PDVO↓ Correlation between counterparty’s asset and underlying stock ↑→ PDVO ？