Pricing Convertible Bonds with Reset Clauses

1. Pricing Convertible Bonds with Reset Clauses Ernst & Young Advisory Limited Su-Yong Sun Ph.D.

2. Outline • Background of our problems • Convertible bond with reset clauses • Snapshot of currently popular methods for pricing convertible bonds in practice • Pointing out the problems related to the aforementioned convertible bond

3. Quantitative Advisory Services Weassist our EY assurance and advisory clients in the Far East Area with the valuation of financial securities and derivatives, verification of pricing methodology, validation of pricing model, testing of risk management models and market data preprocess, and so on.

4. Quantitative Advisory Services • Fixed income securities,such as bonds, loan and convertibles • Interest rate derivatives, such as forwards, swap, caps and floors, swaptions, extendible swaptions, callable snowballs, CMS spread, range accrual swaptions, and other structured interest rate derivatives • Options and exotic options, such as European, American and Bermudan option, barrier, patial barrier and double barrier options, binary and binary barrier options, quanto options, Asian options, average strike options, lookbacks, rainbow options, basket options, etc.

5. Quantitative Advisory Services • Equity derivatives,such as equity swap, warrants, preferred shares, equity index- or basket- linked notes, equity options and exotic options • Commodity and energy derivatives, such as commodity and energy forwards, options, extendible options etc. • Foreign exchange derivatives, such as cross currency swap, swaption, quantos and foreign exchange linked structured products • Credit derivatives, such as CDS, BDS, CLN and CDO, etc.

6. Why convertible bond? • Huge market amount: 1000 billion US dollars in 2006 • Main financing method for Asian company, due to Flexibility for investor Lower financing cost for the company • Up to now the valuation methodology is not complete

7. Convertible bonds- basic features A convertible bond is a type of bond that can converted into shares of stock in the issuing company, As a fixed income security, it involves in • Credit risk As equity-linked security, it is often embeded by • Call option • Put option

8. Convertible bonds- new features • Soft call option. This means the issuer can get the right to call back the bond in a certain period only if some conditions are met. • Rest Clause. This means the conversion price can be adjusted according to some pre-assigned clause.

9. Main terms Issuer: XX company Effective Date: Jul 1, 2006 Maturity Date: Jul 1, 2012 Par: 100,000 TWD Coupon: 0 Conversion Start Date: Sep 1, 2006 Conversion End Date: Jun 1, 2012 Underlying Equity: Common stock of XX company Original Conversion Price: 56.5 TWD

10. Main terms Reset Clause: • Subject to the dilution adjustment • If the arithmetical average of the underlying stock price in 30 business days is less than the 95% of current conversion price then the conversion price is set to Where is the arithmetical average of the underlying stock price of 30 business days, is the current conversion price

11. Main terms Soft call option: If the underlying stock price in successive 20 business days is not less than 150% of the original conversion price then the issuer could buy the bond back with par price

12. Main terms Put option: On each Apr 30 from 2007 to 2009 the bondholder has the right to sell the bond back to its issuer with an annual interest rate 2.5%

13. Existed methods • Closed form solution method: Obtained from mathematical formula directly • PDE method: based on the non-arbitrage theory optimal stopping problem for a game option • Lattice method (tree method): • Monte Carlo method:

14. Monte Carlo method In practice, we use “Least Square Monte Carlo Method” to value a convertible bond with the three above mentioned features, such method was proposed by Longstaff and Schwarts, however there are also some issues for such method in valuing a convertible bond with reset clause

15. Monte Carlo method • Low convergence speed time cost memory cost • Larger simulation variance

16. Our Questions Question 1: From the theoretical point of view: Are there any mathematical models, which can describe the three above mentioned features and also have some good analytic properties? (under some reasonable assumptions)

17. Our Questions Question 2: From the applied point of view: Are there any efficient numerical methods, which can implement such hybrid derivative considering memory and time costs.