R. Merton published a seminal paper [1] that laid the foundation for the development of structural credit risk models. In this post, we’re going to provide an example of how it can be used for managing credit risks. Within the Merton model, equity of a firm is considered a call option on its asset, and…
Read More Credit Risk Management Using Merton ModelIn the previous installment, we presented a concrete example of pricing a European option. In this follow-up post we are going to provide an example of valuing American options. The key difference between American and European options relates to when the options can be exercised: A European option may be exercised only at the expiration…
Read More Valuing an American Option-Derivative Pricing in ExcelAn option is a financial contract that gives you a right, but not an obligation to buy or sell an underlying at a future time and at a pre-determined price. Specifically, … an option is a contract which gives the buyer (the owner or holder of the option) the right, but not the obligation, to…
Read More Valuing a European Option-Derivative Pricing in ExcelLast year, in a post entitled Credit Derivatives-Is This Time Different we wrote about credit derivatives and their potential impact on the markets. Since then, they have started attracting more and more attention. For example, Bloomberg recently reported that collateralized loan obligations (CLO), a type of complex credit derivatives, are becoming a favorite financing vehicle…
Read More Are Collateralized Loan Obligations the New Debt Bombs?The overnight index swap (OIS) has come into the spotlight recently, due to the widening of the Libor-OIS spread. For example, the Economist recently reported: WATCHING financial markets can be like watching a horror film. A character walks into the darkness alone. A floorboard creaks. The latest spooky sign is the spread between the three-month…
Read More Overnight Index Swap DiscountingWe have written many blog posts about the increase in volatility of volatility. See, for example Is Volatility of Volatility Increasing? What Caused the Increase in Volatility of Volatility? Similarly, last week Bloomberg reported, The sudden rise in volatility in February and March showed that even with strong growth fundamentals, financial markets remain vulnerable. Since…
Read More Black Swan and Volatility of VolatilityThe US equity market just reached new highs, and it broke many records. For example, Bloomberg reported that the US market had not been overbought like this in 21 years. The S&P 500 Index’s superlative start to 2018 is making a contrarian technical indicator look silly. The benchmark gauge is poised to end trading Thursday…
Read More Correlation BreakdownThe sell-off in the high yield bond Exchange Traded Funds space last month reminds us of an important risk factor: liquidity. But what exactly is liquidity risk? According to Aleksander Kocic, derivatives strategist at Deutsche Bank AG, Liquidity transforms the risk of default (the ability that the debtor may not be able to pay back…
Read More Liquidity Risk and Exchange Traded FundsPeter Carr recently gave a talk on volatility trading at the Fields institute. Summary: In general, an option’s fair value depends crucially on the volatility of its underlying asset. In a stochastic volatility (SV) setting, an at-the-money straddle can be dynamically traded to profit on average from the difference between its underlying’s instantaneous variance rate…
Read More Volatility, Skew, and Smile TradingValue at Risk (VaR) is an important risk measure that large financial institutions use for managing the risks and allocating capital. Wikipedia defines VaR as follows: Value at Risk (VaR) is a measure of the risk of investments. It estimates how much a set of investments might lose, given normal market conditions, in a set…
Read More Is Value at Risk a Good Risk Measure?