From various empirical work, it is well known that the volatility of asset returns changes over time. This might be one of the reasons that implied volatilities differ for options that only differ in time to maturity. We construct models for the relation between short- and long-term implied volatilities based on three different assumptions of stock return volatility behavior, i.e., mean-reverting, GARCH, and EGARCH models. We test these relations on option price data and conclude that EGARCH gives the best description of asset prices and the term structure of options' implied volatilities.

Option replication is discussed in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black-Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.

ABSTRACT Option replication is discussed in a discrete‐time framework with transaction costs. The model represents an extension of the Cox‐Ross‐Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black‐Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.

We consider nine different proxies (issued amount, listed, euro, on-the-run, age, missing prices, yield volatility, number of contributors and yield dispersion) to measure corporate bond liquidity and use a four-variable model to control for interest rate risk, credit risk, maturity and rating differences between bonds. The null hypothesis that liquidity risk is not priced in our data set of euro corporate bonds is rejected for eight out of nine liquidity proxies. We find significant liquidity premia, ranging from 13 to 23 basis points. A comparison test between liquidity proxies shows limited differences between the proxies.