Technical paper/Volatility
Cutting edge – multi-scale volatility in commodity markets
This paper deals with volatility estimation in commodity markets. Piotr Grzywacz and Krzysztof Wolyniec note that energy commodities have many time (volatility) scales, which has dramatic implications for mean-reversion and volatility estimation. They…
From spot volatilities to implied volatilities
From spot volatilities to implied volatilities
Valuation of with-profit insurance policies with interest rate guarantees
Classical with-profit life insurance products are traditionally backed by a buy-and-hold bond investment strategy. Using book-value accounting for such products tends to lead to a design of the guarantee rate based on an average of long-term interest…
Putting the smile back on the face of derivatives
Cross-asset quadratic Gaussian models have been limited in the scale of their implementation by the difficulty in ensuring the correct drift conditions to omit arbitrage. Here, Paul McCloud shows how to exploit the symmetries of the functional form to…
Pricing with a smile
In the January 1994 issue of Risk, Bruno Dupire showed how the Black-Scholes model can be extended to make it compatible with observed market volatility smiles, allowing consistent pricing and hedging of exotic options
Smiling at convexity
The price of a constant maturity swap (CMS)-based derivative is largely determined by the value of swaption volatilities at extreme strikes. Fabio Mercurio and Andrea Pallavicini propose a simple procedure for stripping consistently implied volatilities…
Time to smile
Cutting edge: Option pricing
Selling risk at a premium
Option strategies
Exotic spectra
Eigenfunction expansions can also be applied to finance. The method is particularly suited to barrier and Asian options, with convergence properties that compare favourably with Monte Carlo.
Great realisations
Volatility estimation
Calibrating random volatility
Stochastic volatility
Volatility swaps made simple
Volatility
If the skew fits
Volatility
Pricing with a smile
Bruno Dupire shows how the Black-Scholes model can be extended tomake it compatible with observed market volatility smiles, allowingconsistent pricing and hedging of exotic options