Calculating risk measures can be extremely time consuming for large portfolios. Monte Carlo and historical value at risk and expected shortfall calculations can require repricing 1,000s of positions 1,000s of times. This makes risk calculations extremely challenging when the pricing functions...

This paper develops a decentralized theory that determines the fair value of the yield-to-maturity of a bond or bond portfolio based purely on the near-term dynamics of the yield itself. The theory decomposes the yield into three components: its expected change, its risk premium, and its...

We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation <X> of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale...</x>