Pricing Convertible Bonds Using PDEs Dragan Bezanovic

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Presentation transcript:

Pricing Convertible Bonds Using PDEs Dragan Bezanovic Leversys –Tesla Solutions and services for financial markets Split, June 2011 1

Solutions and Services Leversys and Tesla Risk Analytics provide financial market clients with innovative and leading edge solutions and services that enable them to leverage their skills and resources. System Solutions Data Services Operation Services Custom Software Development Valuation Models 2

Solutions and Services System Solutions Leversys Drina, cross-asset class system for instrument analytics and portfolio risk management Valuation Models Pricing libraries for convertible bonds, fixed income, equity and credit derivatives Data Services Setup and maintenance of convertible bonds terms and conditions 3

Solutions and Services Custom Software Development Custom development of projects that are not related to Leversys or Tesla solutions. Operation Services Trade capture, confirmation and settlement, positions and cash reconciliation, valuation and P&L reporting, custom reporting, collateral management, documentation management, security master and static data maintenance. 4

Instruments – Coverage and development plan Existing coverage Development pipeline bonds zero coupon, fixed, floating, step up/down, accreting, structured convertibles callable, putable, accreting, resettable, variable conversion, exchangeable PERCS like mandatories PEPS like mandatories convertible asset swaps equity options equity default swaps credit default swaps bonds (PIK, sinking schedule) Convertibles (contingent conversion, dividend protection, takeover protection) options futures FX credit default swap interest rate swaps variance swaps dividend swaps 5

CBs-definition Convertible Bonds (CBs) are bonds that can be converted into a fixed number of shares of the issuer. Convertibles are hybrid securities: - They have the benefits of debt instruments that pay fixed coupons and will be redeemed at maturity at a pre-specified price. - On the other hand, the embedded conversion option provides the investor with a participation in the upside potential of the underlying equity. So, at maturity, the CBs are worth the higher of (a) redemption value (the price at which the issuer had agreed to buy the bonds back) or (b) the value of the underlying shares 6

CBs-definition (cont) 7

CBs-definition (cont) 8

Types of CBs Vanilla CBs Exchangeables Mandatory CBs Contingent convertables Cross FX CBs Resettable CBs and many more… 9

CBs - pricing Underlying equity follows Geometric Brownian Motion with jumps: S(t-) and S(t+) are left and right limits of stock price Wt is a standard Brownian motion, Nt is a Poisson (counting) process When jump occurs we have 10

CBs - pricing Following standard Ito’s calculus, we end up with Black Scholes PDE B(t) is the value recovered in the case of default (B(t)=RR*Notional(t)) 11

Numerical method Crank Nicholson method for time integration Finite difference for spatial discretisation Example (CB Vedanta 2017, price VS spot) 12

Screenshots - Tesla (excel) 13

Screenshots - Drina (CB Analysis) 14

Screenshots - Drina (Portfolio Monitor) 15

References TeslaLib – Model document, Leversys Leversys-Tesla Risk Analytics, Presentation, Leversys, 2011 Marcus Overhaus et al.Equity Hybrid Derivatives, John Wiley and Sons, Inc.,2007 16