Rafal Wojakowski

Dr Rafal Wojakowski

Reader in Finance
PhD (Finance), MRes (Economics), MEng (Mathematical Physics)
+44 (0)1483 683477
08 MS 02
Meetings 1 to 1: Please send me a Calendar invite. Always happy to see you!

Academic and research departments

Surrey Business School.


Areas of specialism


University roles and responsibilities

  • PGR Director, 3-year PhD in Management, Surrey Business School
  • PGR Director, PhD in Finance and Accounting, Department of Finance and Accounting
  • PGR Director, PhD in Healthcare Management, Surrey Business School

    Previous roles

    2013 - 2015
    Research seminar convenor

    Affiliations and memberships

    Member of Advisory Board
    Centre for Quantitative Finance, University of Kent


    Research interests

    My teaching

    My publications


    S Ebrahim, M Shackleton, RM Wojakowski (2008)Valuing Participation Mortgage Loans Using Profit Caps and Floors
    RM Wojakowski, M Shackleton (2001)On Option Expected Returns, In: Mathematical Financepp. 265-374 Birkhauser Verlag
    M Shackleton, RM Wojakowski (2001)Reversible Real Options, In: Mathematical Financepp. 339-344 Birkhauser Verlag
    RM Wojakowski, S Ebrahim, M Shackleton (2009)On Pricing Continuous Workout Mortgages
    F Quittard-Pinon, RM Wojakowski (1994)On Term Structure & Options (Sur la structure par terme & des options) Ecole Normale Supérieure
    RM Wojakowski, S Ebrahim, M Shackleton (2008)Valuing participation mortgage loans using profit caps and floors
    RM Wojakowski (2011)Continuous Workout Mortgages
    Robert J Shiller, Rafal M Wojakowski, M Shahid Ebrahim, Mark B Shackleton (2017)Continuous Workout Mortgages: Efficient Pricing and Systemic Implications, In: Journal of Economic Behavior and Organization Elsevier

    This paper studies the Continuous Workout Mortgage (CWM), a two in one product: a fixed rate home loan coupled with negative equity insurance, to advocate its viability in mitigating financial fragility. In order to tackle the many issues that CWMs embrace, we perform a range of tasks. We optimally price CWMs and take a systemic market-based approach, stipulating that mortgage values and payments should be linked to housing prices and adjusted downward to prevent negative equity. We illustrate that amortizing CWMs can be the efficient home financing choice for many households. We price CWMs as American option style, defaulting debt in conjunction with prepayment within a continuous time, analytic framework. We introduce random prepayments via the intensity approach of Jarrow and Turnbull (1995). We also model the optimal embedded option to default whose exercise is motivated by decreasing random house prices. We adapt the Barone-Adesi and Whaley (1987) (BAW) approach to work within amortizing mortgage context. We derive new closed-form and new analytical approximation methodologies which apply both for pricing CWMs, as well as for pricing the standard US 30-year Fixed Rate Mortgage (FRM).

    Rafal Wojakowski, M. Shahid Ebrahim, Aziz Jaafar, Murizah Osman Salleh (2019)Can a Loan Valuation Adjustment (LVA) Approach Immunize Collateralized Debt from Defaults?, In: Financial Markets, Institutions & Instruments28(2)pp. 141-158 Wiley

    This study focuses on structuring tangible asset backed loans to inhibit their endemic option to default. We adapt the pragmatic approach of a margin loan in the configuring of collateralized debt to yield a quasi-default-free facility. We link our practical method to the current Basel III (2017) regulatory framework. Our new concept of the Loan Valuation Adjustment (LVA) and novel method to minimize the LVA converts the risky loan into a quasi risk-free loan and achieves value maximization for the lending financial institution. As a result, entrepreneurial activities are promoted and economic growth invigorated. Information asymmetry, costly bailouts and resulting financial fragility are reduced while depositors are endowed with a safety net equivalent to deposit insurance but without the associated moral hazard between risk-averse lenders and borrowers.

    MB Shackleton, AE Tsekrekos, R Wojakowski (2004)Strategic entry and market leadership in a two-player real options game, In: Journal of Banking and Finance28(1)pp. 179-201

    We analyse the entry decisions of competing firms in a two-player stochastic real option game, when rivals earn different but correlated uncertain profitabilities from operating. In the presence of entry costs, decision thresholds exhibit hysteresis, the range of which is decreasing in the correlation between competing firms. A measure of the expected time of each firm being active in the market and the probability of both rivals entering within a finite time are explicitly calculated. The former (latter) is found to decrease (increase) with the volatility of relative firm profitabilities implying that market leadership is shorter-lived the more uncertain the industry environment. In an application of the model to the aircraft industry, we find that Boeing's optimal response to Airbus' launch of the A380 super carrier is to accommodate entry and supplement its current product line, as opposed to the riskier alternative of committing to the development of a corresponding super jumbo. © 2002 Elsevier B.V. All rights reserved.

    M Shackleton, RM Wojakowski (2007)Finite Maturity Caps and Floors on Continuous Flows, In: Journal of Economic Dynamics and Control31(12)pp. 3843-3859 Elsevier

    Models of interest rate caps and floors are typically based on discrete rates over finite horizons while existing real option models describe perpetual claims on the maximum of two continuous flows. In this paper, we produce formulae for finite maturity caps and floors that are contingent on continuous flows. We present hedge ratios and discuss applications where a lognormally distributed flow variable is suitable. For other situations where practitioners use proprietary models, the formula presented is useful as a quick, tractable and universal means for mapping quoted implied to prices and vice versa.

    V Henderson, D Hobson, W Shaw, RM Wojakowski (2007)Bounds for In-progress Floating-strike Asian Options Using Symmetry, In: Annals of Operations Research151(1)pp. 81-98 Springer Verlag

    This paper studies symmetries between fixed and floating-strike Asian options and exploits this symmetry to derive an upper bound for the price of a floating-strike Asian. This bound only involves fixed-strike Asians and vanillas, and can be computed simply given one of the many efficient methods for pricing fixed-strike Asian options. The bound is exact until after the averaging has begun and again at maturity. The bound is compared to benchmark prices obtained via Monte Carlo simulation in numerical examples.

    RJ Shiller, RM Wojakowski, S Ebrahim, M Shackleton (2011)Continuous Workout Mortgages, In: National Bureau of Economic Research Working Paper
    R Shiller, RM Wojakowski, S Ebrahim, M Shackleton (2013)Mitigating Financial Fragility with Continuous Workout Mortgages, In: Journal of Economic Behavior and Organization85pp. 269-285 Elsevier
    RM Wojakowski (2012)How Should Firms Selectively Hedge? Resolving the Selective Hedging Puzzle, In: Journal of Corporate Finance18(3)pp. 560-569 Elsevier
    AE Tsekrekos, M Shackleton, RM Wojakowski (2012)Evaluating Natural Resource Investments Under Different Model Dynamics: Managerial Insights, In: European Financial Management18(4)pp. 543-577 Blackwell Publishing
    S Ebrahim, M Shackleton, RM Wojakowski (2011)Participating Mortgages and the Efficiency of Financial Intermediation, In: Journal of Banking and Finance35(11)pp. 3042-3054 Elsevier
    M Chesney, B Marois, RM Wojakowski (1997)Foreign Exchange Options: Pricing (Options de change: evaluation), In: Encyclopaedia of financial markets (Encyclopedie des marches financiers)(69)pp. 1398-1422 Economica
    V Henderson, R Wojakowski (2002)On the equivalence of floating-and fixed-strike Asian options, In: Journal of Applied Probability39(2)pp. 391-394

    There are two types of Asian options in the financial markets which differ according to the role of the average price. We give a symmetry result between the floating- and fixed-strike Asian options. The proof involves a change of numéraire and time reversal of Brownian motion. Symmetries are very useful in option valuation, and in this case the result allows the use of more established fixed-strike pricing methods to price floating-strike Asian options.

    M Shackleton, R Wojakowski (2001)On the expected payoff and true probability of exercise of European options, In: Applied Economics Letters8(4)pp. 269-271

    The continuous-time formula for expected payoff to holding an option, which nests several major pricing tools, is derived. It is shown also that under current market conditions the true exercise probability, N(d4), lies halfway between the two more familiar terms: N(d1) and N(d2).

    RM Wojakowski, S Ebrahim, M Shackleton (2012)Optimal amortization schedule of repayment participation mortgages
    Rafal Wojakowski, M Shahid Ebrahim, MB Shackleton (2016)Reducing the Impact of Real Estate Foreclosures with Amortizing Participation Mortgages, In: Journal of Banking and Finance71pp. 62-74 Elsevier

    We employ Amortizing Participation Mortgage (APM) to offer a novel ex post renegotiation method of a foreclosure. APM belongs to the family of home loan credit facilities advocated in the Dodd-Frank Wall Street Reform and Consumer Protection Act 2010. In our framework, APMs reduce the endemic agency costs of debt by improving affordability. These benefits increase the demand for real estate in bust times and reduce fragility of the financial system thereby preventing foreclosures. We evaluate APMs in a stochastic control framework and provide solutions for an optimal amortization schedule. We generalize our approach to partially amortizing and commercial mortgages which encompass balloon payments. Finally, we provide concrete numerical examples of home loan modifications. We also offer detailed sensitivity analysis to market parameters such as house price volatility and interest rates.

    M Shackleton, R Wojakowski (2002)The Expected Return and Exercise Time of Merton-style Real Options, In: Journal of Business Finance & Accounting29(3&4)pp. 541-555

    We analyse the rate of return and expected exercise time of Merton-style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk-neutral and risk-adjusted pricing techniques, Merton-style options are shown to have an expected return that is a "constant percentage" of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.

    RJ Shiller, RM Wojakowski, S Ebrahim, M Shackleton (2011)On Continuous Workout Mortgages

    Additional publications