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This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Liealgebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

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Merton-type models of pricing corporate bonds based on relatively simple default processes cannot generate credit spreads which replicate empirically observed spreads. This article presents an analytical valuation model of corporate discount bond prices to address this problem. The main feature of the model is a dynamic default barrier. Different default scenarios can be incorporated into the valuation model through adjusting the default barrier's dynamics. We derive a closed-form solution of the corporate bond price based on the model as a function of the firm value and short-term interest rate, with time-dependent model parameters. The numerical results calculated from the solution show that the model is capable of producing term structures of credit spreads that are consistent with some empirical findings. This model could provide new insight for future research on corporate bond analysis and credit risk modeling.

Significant deviations from covered interest parity were observed during the financial crisis of [2007][2008][2009]. This paper finds that before the failure of Lehman Brothers market-wide funding liquidity risk was the main determinant of these deviations measured by swap-implied US dollar (USD) interest rates for the euro, British pound, Hong Kong dollar, Japanese yen, Singapore dollar and Swiss Franc relative to US Libor rates. This evidence suggests that the deviations can be explained by the existence and nature of liquidity constraints. After the Lehman default, both counterparty risk and funding liquidity risk in the European economies were the significant determinants of the positive deviations found for these currencies, while the tightened liquidity condition in the USD was the main driving factor of the negative deviations in the Hong Kong, Japan and Singapore markets. The negative deviations reflect the fact that these markets became alternative dollar funding sources as borrowing in the European economies became more difficult. Federal Reserve Swap lines with other central banks that eased the liquidity pressure reduced the positive deviations in the European economies.