The substrate dependent competitive formation of cyclobutanones and cyclopentanones in an intramolecular rhodium carbenoid CH insertion reaction: enantiospecific total synthesis of silphiperfol-6-ene

The enantiospecific total synthesis of silphiperfol-6-ene has been accomplished starting from the readily available monoterpene (R)-limonene, employing a rhodium carbenoid insertion into the CH bond of a tertiary methyl group. A substrate dependent competitive insertion of the rhodium carbenoid in the gamma- and beta-CH bonds to form cyclopentanone and cyclobutanones, respectively, has been described. (C) 2012 Elsevier Ltd. All rights reserved.

Pricing Defaultable Bonds in a Markov Modulated Market

We address the problem of pricing defaultable bonds in a Markov modulated market. Using Merton's structural approach we show that various types of defaultable bonds are combination of European type contingent claims. Thus pricing a defaultable bond is tantamount to pricing a contingent claim in a Markov modulated market. Since the market is incomplete, we use the method of quadratic hedging and minimal martingale measure to derive locally risk minimizing derivative prices, hedging strategies and the corresponding residual risks. The price of defaultable bonds are obtained as solutions to a system of PDEs with weak coupling subject to appropriate terminal and boundary conditions. We solve the system of PDEs numerically and carry out a numerical investigation for the defaultable bond prices. We compare their credit spreads with some of the existing models. We observe higher spreads in the Markov modulated market. We show how business cycles can be easily incorporated in the proposed framework. We demonstrate the impact on spreads of the inclusion of rare states that attempt to capture a tight liquidity situation. These states are characterized by low risk-free interest rate, high payout rate and high volatility.