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  • Credit Risk Management Using Merton Model
    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 it is expressed as follows,where    E denotes the equity of the firm,               V is the firm’s asset,                is the asset volatility,                B is the notional amount of the debt,               r is the risk-free interest rate, andWe note that both asset (V) and its volatility are not observable. However, the asset volatility can be related to equity and its volatility through the following equation,where denotes the volatility of equity.These 2 equations can be solved simultaneously in order to obtain V and its volatility which are then used to determine the credit spreadHaving the credit spread, we will be able to calculate the probability of default (PD).  Loss given default (LGD) can also be derived under Merton framework.Graph below shows the term structures of credit spread under various scenarios for the leverage ratio (B/V).[caption id="attachment_541" align="aligncenter" width="564"] Term structure of credit spread[/caption]It’s worth mentioning that the Merton model usually underestimates credit spreads. This is due to several factors such as the volatility risk premium, firm’s idiosyncratic risks and the assumptions embedded in the Merton model.  This phenomenon is called the credit spread puzzle.  Research is being conducted actively in order to improve the model.References[1] Merton, R. C. 1974, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, Vol. 29, pp. 449–470. Originally Published Here: Credit Risk Management Using Merton Model
  • Valuing an American Option-Derivative Pricing in Excel
    In 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 date of the option, i.e. at a single pre-defined point in time.An American option on the other hand may be exercised at any time before the expiration date. Read moreAn exact analytical solution exists for European options.  For American options, however, we have to use numerical methods such as Binomial Tree (i.e. Lattice) or approximations.  The post entitled How to Price a Convertible Bond provides an example of the Binomial Tree approach.The Binomial Tree model is an accurate one. However, its main drawback is that it’s slow. Consequently, several researchers have developed approximate solutions that are faster. In this example we’re going to use the Barone-Andesi-Whaley approximation [1].The Barone-Adesi and Whaley Model has the advantages of being fast, accurate and inexpensive to use. It is most accurate for options that will expire in less than one year.The Black-Scholes Model is appropriate for European options, that is, options that may be exercised only on the expiration date. The Barone-Adesi and Whaley Model is designed for American options, which are options that may be exercised at any time before they expire. The Barone-Adesi and Whaley Model takes the value computed by the Black-Scholes Model and adds the value of the early exercise option that is available on American option.. Read more[caption id="attachment_518" align="aligncenter" width="621"] Government of Canada Benchmark Bond Yield. Source: Bank of Canada[/caption]Recall that the important inputs are:VolatilityIn this example we are going to use historical volatility. We retrieve the historical stock data from Yahoo finance.  We then proceed to calculate the daily returns and use them to determine the annual volatility. The resulting volatility is 43%. Detailed calculation is provided in the accompanying Excel workbook.Stock priceThe stock price is also obtained from Yahoo finance. It is 13.5 as of the valuation date (Aug 22 2018).DividendThe dividend yield is obtained from Yahoo finance. It is 1.2%. Note that for illustration purposes we use continuous instead of discrete dividend.Interest rateThe risk-free interest rate is retrieved from Bank of Canada website. Since the tenor of the option is 3 years, we’re going to use the 3-year benchmark yield. It is 2.13% as at the valuation date.We use the Excel calculator again and obtain a price of $3.32 for the American put option.[caption id="attachment_519" align="aligncenter" width="336"] American option valuation in Excel[/caption]Click on the link below to download the Excel Workbook. ReferencesBarone-Adesi, G. and Whaley, R.E. (1987) Efficient Analytic Approximation of American Option Values The Journal  of Finance, 42, 301-320.Article Source Here: Valuing an American Option-Derivative Pricing in Excel
  • VALUING A EUROPEAN OPTION
    An 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 buy or sell an underlying asset or instrument at a specified strike price on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price (market price) of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Read moreExcellent textbooks and papers have been written on options pricing theory; see for example Reference [1]. In this post we are going to deal with practical aspects of pricing a European option. We do so through a concrete example.We’re going to price a put option on Barrick Gold, a Canadian mining company publicly traded on the Toronto Stock Exchange under the symbol ABX.TO.  For this exercise, we assume that the option is of European style with a strike price of $13. (American style option will be dealt with in the next installment). The option expires in 3 years, and the valuation date is August 22, 2018.[caption id="attachment_484" align="aligncenter" width="540"] Barrick Gold mining financial data as at Aug 23 2018[/caption]The important input parameters are:VolatilityIn this example we are going to use historical volatility. We retrieve the historical stock data from Yahoo finance.  We then proceed to calculate the daily returns and use them to determine the annual volatility. The resulting volatility is 43%. Detailed calculation is provided in the accompanying Excel workbook.Stock priceThe stock price is also obtained from Yahoo finance. It is 13.5 as at the valuation date.DividendThe dividend yield is obtained from Yahoo finance. It is 1.2%. Note that for illustration purposes we use continuous instead of discrete dividend.Interest rateThe risk-free interest rate is retrieved from Bank of Canada website. Since the tenor of the option is 3 years, we’re going to use the 3-year benchmark yield. It is 2.13% as at the valuation date.After obtaining all the required input data, we use QuantlibXL to calculate the price of the option. The calculator returns a price of $3.21. The picture below presents a summary of the valuation inputs and results.[caption id="attachment_482" align="aligncenter" width="306"] European option valuation in Excel[/caption]In the next installment, we’re going to present an example for American option.Follow the link below to download the Excel Workbook. References[1] Hull, John C. (2005), Options, Futures and Other Derivatives (6th Ed.), Prentice-Hall Article Source Here: VALUING A EUROPEAN OPTION
  • Separating Good From Bad Emerging Market Exposure
    From WisdomTree: As pioneers of Modern Alpha strategies and currency hedging, WisdomTree has been at the forefront of providing smarter exposure to investors. Our head of Research, Jeremy Schwartz, recently wrote about managing currency risk in our newly launched Emerging Market (EM) multifactor strategy. This comes… Read more ›
  • China Continues To Dump U.S. Treasuries
    From Palisade Research: Earlier this week – news went by relatively unnoticed by the ‘mainstream‘ financial media (CNCB and such) that Beijing’s started selling their U.S. debt holdings. Putting it another way – they’re dumping U.S. bonds. . . “China’s ownership of U.S. bonds,… Read more ›
  • Copper Is Suddenly Breaking Bullish
    From Chris Kimble: Doc Copper over the past few months has been hit hard, as sellers drove it down nearly 25%. This decline brought it to the price point (2), where four different support lines came into play, which looks like… Read more ›
  • The Best High-Yield REITs To Buy Right Now
    From Contrarian Outlook: Real estate investment trusts (REITs) and their typically high dividend yields are a key part of a payout-powered retirement portfolio that’s built to dish out higher and higher dividends every single year. The five REITs we’ll discuss… Read more ›
  • What Sector Reclassifications Mean For Your Favorite ETFs
    From BlackRock: Investors might need to relearn some long-held assumptions following a major reshuffle of stock sector classifications. Leading astronomers made a surprise ruling 12 years ago: Pluto, the smallest planet circling the sun, is not a planet at all. The cosmic… Read more ›
  • Overbought Signals Emerge For The S&P 500
    From Larry McMillan: Stocks had broken out to new all-time highs (at least for $SPX) in late August. Then, a minor correction saw a pullback and test of the breakout level at 2860-2870. That held, and now the market is… Read more ›
  • Invest Alongside These 2 Company Insiders for Yields up to 8.6%
    From Contrarian Outlook: The best way to learn about a company is directly from the executives that run the business on a day-to-day basis. However, there are thousands of actively traded stocks in the U.S. alone and CEOs rarely make… Read more ›
  • Fed funds rate set to rise past inflation for first time since 2008
    Widely expected increase will push key US measure above price rises
  • Why investors should worry about rising wages
    Low wage inflation fuelled the bull market but this is now changing
  • Five reasons why bitcoin fails the innovation test
    Crypto-assets are impractical and do little for financial inclusion
  • China floods debt market with new bond
    Local governments press banks into buying $200bn ‘special-purpose’ securities
  • Investors ignore human rights at their peril
    From land grabs to illegal labour, civil liberties issues should matter to investors
  • Fintech pair aim to disrupt industry with investments for millennials
    New funds from Revolut and Plum will appeal to smartphone generation
  • Record profits for Europe's private banks
    Strong markets boost groups but McKinsey questions ability to sustain growth
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