# Team 7: Valuation of Over-the-Counter Derivatives with Collateralization

More and more over-the-counter (OTC) derivatives traded post-crisis are collateralized in order to reduce counterparty’s credit risk or to be required in clearing houses according to new regulation. In this case, financial institutions need to incorporate the cost to raise capital for funding the collateral request into the traditional (uncollateralized) valuation models to find the fair value of the derivatives, which attracts large amount of attention and interest in funding value adjustment (FVA). If the OTC derivatives are perfectly collateralized, an OIS discounting is sufficient for the correct valuation methodology as pointed out in [5]. However, in practice, collateralization under the credit support annex (CSA) may be imperfect, such that OIS discounting is not necessarily a suitable valuation method any more.

We are planning to perform some quantitative impact study on valuation OTC derivatives with imperfect collateralization. In particular, an interesting topic is the cross currency collateralization, which is widely applied in practice. In the simplest case, the collateral may be posted in a pre-determined currency different from the derivative itself, this may lead to certain quanto effect in valuation [3]. A further study will be for the case that collateral can be chosen among a set of currencies such that the party to post collateral will choose the one with minimum funding cost, which leads to the complexity of the cheapest-to-deliver option similar to bond futures [2]. It is worth noting that this is an American or Bermudan style option, such that one may need to apply the valuation approaches in [1,4]. We will attempt to model these problems, develop valuation methodologies, and obtain some numerical results for the problems during this workshop.

**Prerequisites:**

Stochastic analysis, financial modelling, derivative pricing,

computer coding (C++ or Matlab)

Desired: numerical optimization

**References:**

- L. B. G. Andersen , “A Simple Approach to the Pricing of Bermudan Swaptions in the Multi-Factor Libor Market Model”, March 5, 1999, http://ssrn.com/abstract=155208
- P. Carr, and R. R. Chen, “Valuing bond futures and the quality option”, Technical report, 1997.
- M. Fujii, Y. Shimada, and A. Takahashi, “Collateral Posting and Choice of Collateral Currency – Implications for Derivative Pricing and Risk Management”, May 8, 2010, http://ssrn.com/abstract=1601866
- F. A. Longstaff z and E. S. Schwartz, “Valuing American options by simulation: a simple least-squares approach”, Rev. Financ. Stud. (2001) 14 (1), 113-147.
- V. Piterbarg, “Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing”, Risk Magazine, February 2011, 97–102.