FX Options and Smile Risk

8

Risk Management Tools and Analysis

8.1 INTRODUCTION

In the previous chapters we have analysed specific issues related to the pricing of FX contracts. We have not fully examined the peculiar risks associated with those contracts and how to manage them. The aim of this chapter is to describe some tools to monitor, detect and measure the most relevant risks. Besides, we also show how to employ them in practice and which are the risk profiles, connected to the main types of contracts traded in the FX market, that may be identified by means of them.

The analysis will be carried out along two lines, assuming that we are working either in a BS world or in a stochastic volatility environment. Each of the two cases entails specific risks that should be managed. As we know from Chapter 2, there are many stochastic volatility models but we presented just a few of them that can be used to price FX options. In this chapter we will choose the LMUV model, in its extended version, as an example of how to run an FX option book in a stochastic volatility setting. The reasons for this choice are manifold: we just hint here at the fact that the LMUV is very easy to implement and it allows a closed-form pricing also for exotic contracts whenever corresponding closed-form formulae are available in the BS model.

We start with a brief description of how to implement the LMUV model and calibrate it to a given set of market data.

8.2 IMPLEMENTATION OF THE LMUV MODEL

We assume that the exchange ...