Salih N. Neftci

Tools for Volatility Engineering, Volatility Swaps, and Volatility Trading

This chapter provides an introduction to a sector that may, in the future, play an even more significant role in financial market strategies. The purpose is to show how one can isolate the volatility of a risk factor from other related risks, and then construct instruments that can be used to trade it. Liquid instruments that involve pure volatility trades are potentially very useful for market participants who have natural exposure to various volatilities in their balance sheet or trading book. When a trader takes a position or hedges a risk, he or she expects that the random movements of the underlying would have a known effect on the position. The underlying may be random, but the payoff function of a well-defined contract or a position has to be known. Payoff functions of most classical volatility strategies are not invariant to underlying risks, and most volatility instruments turn out to be imperfect tools for isolating this risk. Even when traders anticipations come true, the trader may realize that the underlying volatility payoff functions have changed due to movements in other variables. Hence, classical volatility strategies cannot provide satisfactory hedges for volatility exposures. The reason for this and possible solutions are given in the chapter.

Dynamic Replication Methods and Synthetics Engineering

This chapter explains the differences between static and dynamic replication. It reviews static replication in the context of bond immunization. We then introduce dynamic hedging in the context of hedging bond positions before moving on to dynamic replication of options using binomial trees. We highlight the distinction between dynamic replication in continuous and discrete time and discuss real-life complications such as bid–ask spreads, jumps, maintenance and operation costs as well as changes in volatility.

Introduction to Interest-Rate Swap Engineering

This chapter expands on the concept of swaps, outlined in the introductory chapter, and their replication. It applies the concept to fixed-income instruments. We discuss the replication of plain vanilla interest-rate swaps. An interest-rate swap can be used to synthetically create its component parts, such as floating rate notes. Analogies to the replication of other swaps, such as equity swaps, are highlighted. The real-world uses of interest-rates swaps are discussed. Real-world complications such as transaction costs are illustrated in an interest-rate swap application involving a new bond issue. Several uses of swaps are discussed in different asset class and the role of taxes and regulation is highlighted.

Institutional Aspects of Derivative Markets

The objective of this chapter is to provide the reader with the necessary practical understanding of financial market conventions and institutional aspects to understand financial engineering. Eurocurrency markets and the differences between onshore and offshore markets are explained. Concepts such as trading, clearing, and settlement are introduced. Recent financial regulation regarding the trading and clearing of derivatives and its importance for financial engineering are discussed.

Counterparty Risk, Multiple Curves, CVA, DVA, and FVA

The objective of this chapter is to introduce the reader to recent innovations and market practice in financial engineering and derivatives pricing related to counterparty risk. Counterparty risk is intimately related to the cost and funding of derivatives transactions and the market maker perspective that we take throughout this book. We introduce adjustments to the default-free value of derivative contracts from the perspective of a bank to reflect the credit risk of the bank’s counterparty (credit valuation adjustment or CVA) and the own credit risk of the bank (debit valuation adjustment or DVA). CVA is shown to resemble an option on the residual value of the portfolio with a random maturity given the default time of the counterparty. We discuss how the default probability can be estimated based on CDS prices, for example. We introduce funding value (adjustment) which reflects the entity’s funding cost. We present recent case studies and numerical examples to illustrate CVA valuation in practice. We discuss CVA hedging, contingent CDS and the role of credit support annexes and so-called CVA desks. We discuss recent changes in market practice such as overnight swap index discounting and point to the recent debate regarding funding valuation adjustment and the choice of the riskless rate proxy.

Cash Flow Engineering, Interest Rate Forwards and Futures

In this chapter, we present the first detailed application of financial engineering tools in the form of simple interest rate derivatives and develop our first contractual equation. First, we introduce the yield curve and its construction as well as market conventions for yield quotations. Then we discuss LIBOR, other benchmark interest rates and the TED spread. We developed our first contractual equation. This equation is manipulated to obtain synthetic loans, synthetic deposits, and synthetic spot transactions. We describe the replication of forward loans using bond and money market instruments, respectively. We build on this discussion to introduce forward on interest rates and explain how forward rate agreements (FRAs) can be replicated. Forward rates, the term structure of interest rates and strips are discussed. We introduce risk measures such as DV01, duration, convexity, value-at-risk and expected shortfall. Finally, we compare OTC and exchange traded fixed income instruments such as Eurocurrency futures .

Securitization, ABSs, CDOs, and Credit Structured Products

In this chapter, we introduce securitization, asset-backed securities (ABSs), and collateralized debt obligations (CDOs). We discuss the economic rationale for securitization and highlight similarities between ABSs and CDOs. The role of CDOs in the GFC and recent regulatory developments affecting securitization are discussed. The valuation of CDO tranches and the link of CDO tranche prices to default correlation are explained. The concept of correlation trading is introduced in this chapter and elaborated upon in the next chapter. We discuss different credit indices such as ABX and LCDX as well as a range of credit structured products including credit options, constant maturity default swap, leveraged super senior notes and contingent convertibles (CoCos). The chapter shows how financial engineering principles and three different valuation approaches can be applied to price CoCos.

Cash Flow Engineering and Alternative Classes (Commodities and Hedge Funds)

In this chapter, we discuss two main topics. The first is an application of cash flow engineering to alternative asset classes such as commodities. This allows us to further broaden our understanding of forward and futures markets to include concepts such as convenience yield, backwardation, and contango. Storage costs of commodities are a real-world complication that needs to be taken into account in commodities cash flow engineering. Following the discussion of commodity futures pricing and replication of commodity futures, we apply the swap engineering methodology that we developed earlier to price and replicate commodity swaps. Hedge funds are one of the most important types of arbitrageurs in liquid markets, and throughout the book we refer to their activities as examples of financial engineering. We provide background on hedge fund strategies and prime brokerage. Recent regulation and the GFC have significantly transformed and institutionalized the hedge fund industry and imply that many views about the industry have to be updated.

Engineering of Equity Instruments and Structural Models of Default

In this chapter, we discuss how financial engineering and option pricing principles can be used to value equity and equity-linked products. We first review the structural models of default and show how they can be used to link bond, CDS, and equity markets. We discuss the different uses of the basic Merton (1974) model to calculate the value of equity, to back out implied credit spreads, or to back out an implied equity volatility. We show how the Merton model is applied in practice to inform capital structure arbitrage strategies. Next, we introduce another class of bonds with embedded options in the form of convertible bonds. Convertible bonds can be decomposed into a straight debt component and a call option and we show how the decomposition can be used for so-called convertible bond arbitrage strategies. We discuss the sources of profits in capital structure and convertible bond arbitrage strategies and contract the role implied volatility and draw conclusions about the relative riskiness of the two classes of strategies. Finally we discuss warrants and uses of convertible bonds in practice.

Correlation as an Asset Class and the Smile

In this chapter, we deal with correlation trading and more advanced aspects of volatility trading. First, we explain how dispersion trades and correlation swaps can be used to generate correlation exposure. Then we discuss the pricing and synthetic replication of correlation swaps. We introduce dirac functions and show their usefulness in analyzing the dependence of the option price on the volatility of the underlying around the strike price. We use Tanaka’s formula to show how option prices can be related to gamma gains. The Breeden–Litzenberger theorem is shown to link risk-adjusted probabilities to arbitrage-free option prices. We use the dirac delta function to prove the theorem. The volatility smile is shown to differ between equity, FX, and fixed-income markets. We explain the implications of the volatility smile for option price, hedging, and trading. We discuss how to trade the smile and how it affects the pricing of exotic options.