The pricing accuracy and pricing performance of local volatility models depends on the absence of arbitrage in the implied volatility surface. An input implied volatility surface that is not arbitrage-free can result in negative transition probabilities and consequently mispricings and false greeks. We propose an approach for smoothing the implied volatility smile in an arbitrage-free way. The method is simple to implement, computationally cheap and builds on the well-founded theory of natural smoothing splines under suitable shape constraints.

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Arbitrage-free smoothing of the implied volatility surface

This paper provides an industry standard on how to quantify the shape of the implied volatility smirk in the equity index options market. Our local expansion method uses a second-order polynomial to describe the implied volatility–moneyness function and relates the coefficients of the polynomial to the properties of the implied risk-neutral distribution of the equity index return. We present a formal, two-way representation of the link between the level, slope and curvature of the implied volatility smirk and the risk-neutral standard deviation, skewness and excess kurtosis. We then propose a new semi-analytical method to calibrate option-pricing models based on the quantified implied volatility smirk, and investigate the applicability of two option-pricing models.

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The implied volatility smirk

Solving an inverse parabolic problem by optimization from final measurement data

An inverse problem of identifying the coefficient of parabolic equation

Without requiring the existence of an equivalent risk-neutral probability measure this paper studies a class of one-factor local volatility function models for stock indices under a benchmark approach. It is assumed that the dynamics for a large diversified index approximates that of the growth optimal portfolio. Fair prices for derivatives when expressed in units of the index are martingales under the real-world probability measure. Different to the classical approach that derives risk-neutral probabilities the paper obtains the transition density for the index with respect to the real-world probability measure. Furthermore, the Dupire formula for the underlying local volatility function is recovered without assuming the existence of an equivalent risk-neutral probability measure. A modification of the constant elasticity of variance model and a version of the minimal market model are discussed as specific examples together with a smoothed local volatility function model that fits a snapshot of S&P500 in...

Local volatility function models under a benchmark approach

This paper presents a new algorithm to calibrate the option pricing model, i.e. the algorithm that recovers the implied local volatility function from market option prices in the optimal control framework. A unique optimal control is shown to exist. Our algorithm is well-posed. Our numerical experiments show that, with the help of the techniques developed in the field of optimal control, the local volatility function is recovered very well.

A new well-posed algorithm to recover implied local volatility

Exploring carbon rebound effects in Chinese households’ consumption: A simulation analysis based on a multi-regional input–output framework

Using the Chinese economic policy uncertainty (EPU) index, this paper investigates the spillover effect on the price pass-through effect of the RMB exchange rate and uncertainty, using the time-varying parameter vector autoregressive (TVP-VAR) model. We find that EPU has a significant effect on the price pass-through effect of the RMB exchange rate, which indicates that an increase in uncertainty will significantly enhance the price pass-through effect of the exchange rate. In addition, EPU itself can have a significant spillover effect on the exchange rate. Finally, the price pass-through effect of the RMB exchange rate is incomplete, and its impact on the price level gradually decreases along the circulation chain. The Chinese government should pay close attention to the impact of economic policy uncertainty on the price pass-through effect of the RMB exchange rate and the exchange rate and further strengthen the risk prevention and early warning mechanism to minimize the impact of uncertainty on China's macroeconomy. • The price pass-through effect of the RMB exchange rate and the spillover effect of uncertainty on the exchange rate are analyzed from the uncertainty's perspective. • Uncertainty has a significant impact on the price pass-through effect of the RMB exchange rate. • The price pass-through effect of the exchange rate will also be affected by macroeconomic performance and inflation. • The price pass-through effect of the RMB exchange rate is incomplete, and its impact on price levels gradually decreases along the circulation chain. 

Lijun Wang

Papers

A new well-posed algorithm to recover implied local volatility

Exploring carbon rebound effects in Chinese households’ consumption: A simulation analysis based on a multi-regional input–output framework

Economic policy uncertainty and price pass-through effect of exchange rate in China