The Convertible Bond Pricing Solution
The Equity Derivatives Pricing Expert

Opscore is our complete front-office solution for the pricing, hedging and analysis of convertible securities. According to Sheen Kassouf and Edward Thorp (co-authors of Beat the Market), a convertible security is “any security that may be exchanged for common stock”. In addition to warrants, Kassouf and Thorp's classification includes convertible bonds, convertible preferred stocks, calls, stock rights and stock options. Opscore consists of three components:

    Opscore GUI
    Figure 1: Click image to enlarge

    The clauses of convertible securities can be so complex that their accurate treatment not only necessitates pricing engines as evolved as ours, but also requires referring to the prospectus as the only reliable and complete source of information.

    For this reason, we maintain a continuously evolving database schema for the terms and conditions of convertible securities. Each time we add a new feature to our pricing engine (after some newly released prospectus), we release the updates of both the pricing engine and the data model.

    Terms and conditions can be edited through a graphical user interface, as shown in Figure 1, and stored in the database. The user can also create and define terms and conditions for new issues of convertible securities.

    The data model of Opscore covers convertible bonds, mandatories, equity options and CB callable asset swaps as shown in Figure 2. Terms and conditions of credit default swaps (CDS) are also handled, as they are needed for the calibration of the default component of the equity-to-credit process.

    Opscore GUI
    Figure 2: Click image to enlarge

    This is the heart of Opscore and the core of our expertise. The pricing engine is the numerical solver of the equity-to-credit Partial Differential Equations (PDE) with the terms and conditions of the given derivative instrument acting as boundary conditions. Our implementation relies on the most advanced finite difference schemes. These schemes include computational grids that adapt in order to best capture the events, whether in time or space, that occur during the lifetime of the specific instrument.

    Inputs to the pricing engine are the terms and conditions of the instruments involved in the pricing, market data (yield curves, stock spot price and FX rates), market assumptions (dividend forecast and recovery rates for each instrument involved on pricing and calibration) and the theoretical parameters (Brownian volatility, hazard rate) which are inferred from the calibration routines, themselves an integral part of the pricing engine.

    Programmed in C++, the pricing engine can be exploited as a separate suite of DLLs (Dynamic-Link Libraries) which the user may wish to integrate into his/her exisiting system, independently of the database schema of Opscore or the Excel functionality. To this end, COM, Java and C++ interfaces are available. The DLL can also be called from Matlab. The client, therefore, can choose between integrating our DLLs into his/her system or relying on us to maintain the databases schema.


    Since Excel is probably the most popular front end among traders and hedge fund managers, we made sure that all the results of Opscore are published to Excel. There are two ways the user may view these results:

    • Using Microsoft Office Automation, the user can export all the terms and conditions of the convertible security from the Opscore data model to the Opscore Excel Analyzer. Several theoretical models can be defined and simulated on this worksheet. 3D surfaces of theoretical values and Greeks can be instantaneously plotted. More generally, every single output can be plotted as a function of every single input. This is achieved by the VBA routines of the Opscore Excel Analyzer, which, in turn, call the DLL of the pricing engine; moreover, the user can simulate terms and conditions different from the ones that are stored in the Opscore database, without affecting the stored data.

    • Alternatively, users can build their own Excel spreadsheet, laying out the results of the pricing engine any way they please thanks to the Opscore XLL functions. The Opscore XLLs accept the identification number of the given security (its internal database code, ISIN, CUSIP, Bloomberg number or SEDOL) as an argument. This allows the XLLs to retrieve the corresponding terms and conditions from the Opscore database. The remaining arguments are the theoretical parameters (such as Brownian volatility and hazard rate). They are produced on the spreadsheet, either by calibration routines or by direct user input.


Opscore offers key benefits for convertible bond users:

    • Accurate pricing, reliable computation of Greeks (speed is of the essence)
    • User friendly Excel toolkit (customizable portfolio screening)
    • Multi-threading (prevents freezes and extracts full power from multi-core CPUs)
    • Access to a database of more than a thousand existing CBs (with updates for new issues)
    • Consistent calibration and pricing of the Equity to Credit derivatives on a single issuer (options, CDS, CBs, …)
    • Joint dynamic hedging of the equity and credit risk components with two instruments (typically the underlying and a CDS or an OTM put)
    • Identification of mispricings and trading opportunities through the precise evaluation of the complex features of the CB (resettable bonds, ASCOTs, takeover protection, dividend protection, …)
    • Fast generation of multiple scenarios of CB prices and Greeks for extended spot ranges at various dates
    • Easy integration in various systems and environments due to well designed multiple interfaces (Java, .NET, C++, Excel)
    • Computation of event probabilities and expected times (conversion, call, put, etc.)
    • Fine tuning of the key parameters of the CB (worst and best terms for coupon, premium, …)
    • Possibility to activate or disable features (calls, puts, triggers, …) and see how they affect the price and the Greeks
    • Handling of complex clauses to optimally fit the objectives of the issuer
    • Accurate computation of implied volatility, spread and YTM

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