Bank of America Merrill Lynch

About: Bank of America Merrill Lynch is a based out in . It is known for research contribution in the topics: Implied volatility & Volatility smile. The organization has 75 authors who have published 126 publications receiving 2825 citations.

No-dynamic-arbitrage and market impact

Abstract: Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that, empirically, these inequalities are typically close to being equalities.

Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Pricing

Abstract: The standard approach (e.g. Dupire (1994) and Rubinstein (1994)) to fitting stock processes to observed option prices models the underlying stock price as a one-factor diffusion process with state- and time-dependent volatility. While this approach is attractive in the sense that market completeness is maintained, the resulting model is often highly non-stationary, difficult to fit to steep volatility smiles, and generally is not well supported by empirical evidence. In this paper, we attempt to overcome some of these problems by overlaying the diffusion dynamics with a jump-process, effectively assuming that a large part of the observed volatility smiles can be explained by fear of sudden large market movements ("crash-o-phobia"). The first part of this paper derives a forward PIDE (Partial Integro-Differential Equation) satisfied by European call option prices and demonstrates how the resulting equation can be used to fit the model to the observed volatility smile/skew. In the second part of the paper, we discuss efficient methods of applying the calibrated model to the pricing of contingent claims. In particular, we develop an ADI (Alternating Directions Implicit) finite difference method that is shown to be unconditionally stable and, if combined with FFT (Fast Fourier Transform) methods, computationally efficient. The paper also discusses the usage of Monte Carlo methods, and contains several detailed examples from the S&P500 market. We compare pricing results obtained by the jump-diffusion approach with those of pure diffusion, and find significant differences for a range of popular contracts.

Volatility Skews and Extensions of the Libor Market Model

Abstract: This paper considers extensions of the Libor market model (Brace et al (1997), Jamshidian (1997), Miltersen et al (1997)) to markets with volatility skews in observable option prices. We expand the family of forward rate processes to include diffusions with non-linear forward rate dependence and discuss efficient techniques for calibration to quoted prices of caps and swaptions. Special emphasis is put on generalized CEV processes for which exact closed-form expressions for cap prices are derived. We also discuss modifications of the CEV process which exhibit appealing growth and boundary characteristics. The proposed models are investigated numerically through Crank-Nicholson finite difference schemes and Monte Carlo simulations.

The Equilibrium Real Funds Rate: Past, Present and Future

Abstract: We examine the behavior, determinants, and implications of the equilibrium level of the real federal funds rate, defined as the rate consistent with full employment and stable inflation in the medium term We draw three main conclusions First, the uncertainty around the equilibrium rate is large, and its relationship with trend GDP growth much more tenuous than widely believed Our narrative and econometric analysis using cross-country data and going back to the 19th Century supports a wide range of plausible central estimates for the current level of the equilibrium rate, from a little over 0% to the pre-crisis consensus of 2% Second, despite this uncertainty, we are skeptical of the “secular stagnation” view that the equilibrium rate will remain near zero for many years to come The evidence for secular stagnation before the 2008 crisis is weak, and the disappointing post-2008 recovery is better explained by protracted but ultimately temporary headwinds from the housing supply overhang, household and bank deleveraging, and fiscal retrenchment Once these headwinds had abated by early 2014, US growth did in fact accelerate to a pace well above potential Third, the uncertainty around the equilibrium rate implies that a monetary policy rule with more inertia than implied by standard versions of the Taylor rule could be associated with smaller deviations of output and inflation from the Fed’s objectives Our simulations using the Fed staff’s FRB/US model show that explicit recognition of this uncertainty results in a later but steeper normalization path for the funds rate compared with the median “dot” in the FOMC’s Summary of Economic Projections

Moment Explosions in Stochastic Volatility Models

Abstract: In this paper, we demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than one can become infinite in finite time. As arbitrage-free price computation for a number of important fixed income products involves forming expectations of functions with super-linear growth, such lack of moment stability is of significant practical importance. For instance, we demonstrate that reasonably parameterized models can produce infinite prices for Eurodollar futures and for swaps with floating legs paying either Libor-in-arrears or a constant maturity swap (CMS) rate. We systematically examine the moment explosion property across a spectrum of stochastic volatility models. Related properties such as the failure of the martingale property, and asymptotics of the volatility smile are also considered.