Derivative Valuation Risk Management

We discuss ways to determine the dividend yield accurately. We use traded options to determine the implied dividend yield. Specifically, if the options are of European-style exercise, then we can use the put-call parity to create a synthetic single stock future. #dividend #investing #excel #finance #income #option #trading

We use the Exponential Weighted (EW) historical volatility that assigns bigger weights to the recent returns, and smaller weights to the past ones. The EWHV is more responsive than the equally weighted historical volatility. Also, the decline of the EWHV from its peak is smoother than that of the equally weighted HV. #volatility #trading #investing #risk #finance #excel #python

We are going to perform some numerical experiments. Specifically, we are going to use the portfolio optimization program developed in the previous post in order to study the effect of diversification. #derivative #trading #risk #python #investing #finance #gold

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The results indicate that there is a mispricing, but it is not an underpricing as widely reported but rather an overpricing. The profitability of the strategy was shown to largely depend on avoiding rich bonds and delta hedging those bonds with a well-defined, or consistent, implied volatility term structure. The common contention that convertible arbitrage is a gamma trading strategy was shown to be incorrect. Arbitrage is a vega trade that is profitable when implied volatilities increase. #derivative #trading #risk #bond #arbitrage #convertible #volatility

Modern Portfolio Theory introduces the concept of an efficient frontier. An efficient frontier represents a set of portfolios that maximize the expected returns for each level of risk or standard deviation. For every level of return that investors expect, there is an #investment that can offer them the lowest standard deviation. Similarly, for every level of risk, there is a #portfolio that gives the highest return. #risk #diversification #investing #trading #finance

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#derivative #trading #risk In this post, we are going to discuss valuation of a callable bond. We chose the Hull-White model to describe the interest rate dynamics. We then use a Python program to build a trinomial tree for the risk-free rates #hedge #python #investment #bond

With a sudden increase in volatility during the pandemic, many volatility funds lost money. Many funds were struck because they adopted a strategy known as shorting volatility betting that it will fall or remain low. Such funds sell derivative protection such as put options, which give the buyer the right to sell at a pre-determined price. They earn money by effectively writing market insurance, hoping that volatility which helps determine options prices will remain low and the options will expire worthless. #stock #option #quant #risk #investing #trading #volatility #hedge http://tech.harbourfronts.com//short-volatility-funds-los/

The trend in the increased holding of risky assets continues. Because of Covid-19, the big banks now hold more illiquid, opaque assets than before. #debt #bond #loan #mortgage #risk #investing #equity http://tech.harbourfronts.com//banks-hold-many-illiquid-a/

Convertible bond issuance has increased during the Covid 19 pandemic. From a funding perspective, convertible bonds have many attractive features for corporates, which have become more important during the pandemic. Despite their attractive features, when investing in convertible bonds, investors should pay particular attention to the credit risks of the issuers and the sector in general. #debt #bond #loan #mortgage #risk #investing #equity... http://tech.harbourfronts.com//convertible-bond-issuance-/

How do you determine the volatility of an unlisted entity, and more generally, how do you forecast volatility? These are non-trivial questions. #volatility #stock #vix #trading #quant #algorithmic #vxx http://tech.harbourfronts.com//forecast-implied-volatility/

A warrant is a financial derivative instrument that is similar to a regular stock option except that when it is exercised, the company will issue more stocks and sell them to the warrant holder. The valuation of warrants is similar to the valuation of stock options except that the effect of dilution should be considered. In this post, we first look at the valuation of warrants without the dilution effect. After that, we will discuss the valuation model that takes dilution into account. #stock #option #quant #risk #investing #trading #volatility #warrant http://tech.harbourfronts.com//valuation-warrants-derivat/

When constructing a portfolio, adding a low correlation, low Sharpe ratio strategy can have the same impact as adding a high Sharp ratio strategy. The low correlation strategy is a great diversifier. The core argument presented in this paper that SR is a misleading index of whom a fund should hire or fire seems at odds with standard business practices. The SR Indifference Curve shows that even PMs with a negative individual SR should be hired if they contribute enough diver...sification. Why is that not the case? Because of a netting problem: A typical business agreement is that PMs are entitled to a percentage of their individual performance, not a percentage of the funds performance. Legal clauses may release the fund from having to pay a profitable PM if the overall fund has lost money, however that PM is unlikely to remain at the firm after a number of such events. This is a very unsatisfactory situation, for a number of reasons: First, funds are giving up the extra-performance predicted by the SR Indifference Curve. Second, funds are compelled to hire star-PMs, who may require a high portion of the performance fee. Third, funds are always under threat of losing to competitors their star-PMs, who may leave the firm with their trade secrets for a slightly better deal. In some firms, PMs turnover is extremely high, with an average tenure of only one or two years. #stock #option #finance #market #trading #investing #risk #quant http://tech.harbourfronts.com//impact-low-correlation-tra/ See more

Performance share units are hypothetical share units that are granted to you based mainly on corporate and/or individual performance. Structurally, they are very similar to restricted stock units except these are more focused on your performance. They are designed to mirror share ownership and you will generally be granted additional units having the same value as dividends being paid on the regular shares. #stock #option #finance #market #trading #investing #risk http://tech.harbourfronts.com//performance-share-units-de/

Valuation of Employee Stock Options is different from regular stock options. In this post, we are going to implement the approach proposed by Hull and White. Specifically, we are going to implement the vesting and forfeiture rate features. Other features can also be implemented without difficulty #stock #option #quant #risk #investing #trading #volatility http://tech.harbourfronts.com//employee-stock-options-der/

We are going to present a method for valuing American options using Monte Carlo simulation. This method will allow us to implement more complex option payoffs with greater flexibility, even if the payoffs are path-dependent. Specifically, we use the Least-Squares Method of Longstaff and Schwartz in order to take into account the early exercise feature. The stock price is assumed to follow the Geometrical Brownian Motion. #python #excel #derivative #trading #investing #finance #investment http://tech.harbourfronts.com//valuing-american-options-u/

We present an extension of the Garman-Klass volatility estimator that also takes into consideration overnight jumps. Garman-Klass-Yang-Zhang (GKYZ) volatility estimator consists of using the returns of open, high, low, and closing prices in its calculation. It also uses the previous days closing price. #volatility #trading #investing #excel #python #derivative #stock http://tech.harbourfronts.com//garman-klass-yang-zhang-hi/

In the previous post, we introduced the Parkinson #volatility estimator that takes into account the high and low prices of a #stock. In this follow-up post, we present the Garman-Klass volatility estimator that uses not only the high and low but also the opening and closing prices. #risk #hedge #quant #trading #investing #finance #vix Garman-Klass (GK) volatility estimator consists of using the returns of the open, high, low, and closing prices in its calculation... http://tech.harbourfronts.com//garman-klass-volatility-ca/

A disadvantage of using the CCHV is that it does not take into account the information about intraday prices. The Parkinson volatility extends the CCHV by incorporating the stocks daily high and low prices. #volatility #quant #trading #vix #risk #hedging #stock http://tech.harbourfronts.com//parkinson-historical-volat/

There are various types of historical volatilities such as close to close, Parkinson, Garman-KIass, Yang-Zhang, etc. In this post, we will discuss the close-to-close historical #volatility. #trading #vix #option #quant #python The CCHV has the following characteristics:... Advantages It has well-understood sampling properties It is easy to correct bias It is easy to convert to a form involving typical daily moves Disadvantages It is a very inefficient use of data and converges very slowly http://tech.harbourfronts.com//close-close-historical-vol/

In #finance, #beta measures a stocks #volatility with respect to the overall market. It is used in many areas of financial analysis and investment, for example in the calculation of the Weighted Average Cost of Capital, in the Capital Asset Pricing Model and market-neutral #trading. #investing #volatility #facebook #spy #python http://tech.harbourfronts.com//stock-beta-calculate-stock/

The #VIX index is an important market indicator that everyone is watching. #VVIX, on the other hand, receives less attention. In this post, we are going to take a look at the relationship between the VIX and VVIX indices. #volatility #correlation #trading #vxx #hedging #risk http://blog.harbourfronts.com//correlation-vvix-vix-indic/

Basic method for calculating VaR is implemented in #Python. To better take into account the tail risks more advanced approaches such as Expected Tail Loss should be used. #risk #trading #quant #hedge http://tech.harbourfronts.com//value-risk-financial-risk-/

New Zealand banks aggressively sold swaps to farmers as a supposedly less risky alternative to fixed interest loans, and a way for farmers to protect themselves from hikes in their mortgage repayments if interest rates went up. But after the financial crisis, up to 2000 New Zealand farmers lost up to $1 billion on swaps. They lost farms they had inherited from their fathers and planned to pass onto their children. Too many committed suicide. #finance #trading #mortgage #loan #farmer #bank #swap http://tech.harbourfronts.com//another-misuse-financial-d/

To price the options, we first simulate the price paths using the following Stochastic Differential Equation. The simulation is carried out until the options maturity. We then apply the terminal payoff functions and calculate the mean values of all the payoffs. Finally, we discount the mean values to the present and thus obtain the option values. #trading #investing #volatility #investment #derivative #python #excel http://tech.harbourfronts.com//valuing-european-options-u/

In this post, we focus on the implementation of the Black-Scholes-Merton option pricing model in Python. Closed-form formula for European call and put are implemented in a Python code. We compare the results to the ones obtained by using third-party software and notice that they are in good agreement. #python #derivative #trading #option #volatility #investing #excel http://tech.harbourfronts.com//black-scholes-merton-optio/

The trend in securitizing loans is upward. Nowadays, not only performing loans but also non-performing loans are being securitized and sold to investors. There are many issues associated with managing the risks of these non-performing loans, notably the lack of standard definitions and valuation methodology. #loan #debt #bond #investing #investment #mortgage #valuation http://tech.harbourfronts.com//collateralized-loan-obliga/

Valuing a Convertible #Bond- #Derivative Pricing in #Python #risk #riskmanagement #TLT #option #quant #trading #VIX #volatility In a previous post, we presented a theoretical framework for pricing convertible bonds and preferred shares. We also provided an example of pricing a convertible bond in Excel. In this installment, we present an example of pricing a convertible bond in Python. http://tech.harbourfronts.com//valuing-convertible-bond-d/

As negative interest rates started popping up around the world, quantitative analysts and traders have been asking a mundane but fundamental question: How to price trillions of dollars of financial instruments when their complex pricing models dont work with negative numbers? #trading #derivative #risk #riskmanagement #quant #finance Intuitively, we would say that negative interest rates will affect the prices of interest-rate sensitive instruments such as interest rate swap...s and swaptions the most. As far as equity derivatives are concerned, the impact will not be as dramatic as with interest-rate sensitive instruments. However, some subtleties in the mathematical approaches can still have an impact on the accuracy of equity-derivative valuation models. http://tech.harbourfronts.com//how-negative-interest-rate/

Investors in South Korea have lost money in a complex #derivative linked to constant maturity #swap. In search for higher yields, they are also putting money into another complex financial instrument, convertible #bonds. #risk #volatility #hyg #tlt #debt http://tech.harbourfronts.com//convertible-bonds-really-a/

Such derivative products are structured to track the performance of constant maturity swap, or a swap that allows the purchaser to fix the duration of received flows on a swap, of Treasury bonds of the United States and Britain and the yield of Germanys 10-year state bonds. #trading #derivative #risk #riskmanagement #quant #finance http://tech.harbourfronts.com//complex-derivative-linked-/

Data compiled by Ned Davis Research shows the S&P 500 would be 19% lower between 2011 and the first quarter of 2019 without buybacks #SPX #VIX #trading #investing #quant http://link.eu5.net/6odu

Stationarity and Autocorrelation Functions of #VXX Time Series Analysis in #Python #trading #investing #quant #VIX #SPX #Volatility #SKEW #VXXB http://tech.harbourfronts.com//stationarity-autocorrelati/

#Mortgage Investors Cool on Swaps as Rush for Duration Ends #hedge #loan #riskmanagement http://link.eu5.net/zdpv

A Volatility Trading System-Time Series Analysis in #Python #trading #investing #quant #VIX #SPX #Volatility #SKEW #VXXB http://tech.harbourfronts.com//volatility-trading-system-/

Huge Stock #Bond #Volatility Disconnect May Not Mean #VIX Explosion #trading #investing #quant #TLT #SPX #loan #SKEW http://link.eu5.net/6d9j

When trading options, we often use the VIX index as a measure of volatility to help enter and manage positions. This works most of the time. However, there exist some differences between the VIX index and at-the-money implied volatility (ATM IV). In this post, we are going to show such a difference through an example. Specifically, we study the relationship between the implied volatility and forward realized volatility (RV) [1] of SP500. We utilize data from April 2009 to December 2018. #trading #investing #quant #VIX #SPX #Volatility #SKEW #riskmanagement #derivative http://blog.harbourfronts.com//differences-vix-index-mone/

An almost complete recovery in credit markets since the sell-off late last year and a dovish Federal Reserve are refocusing attention on the multiyear boom in corporate #debt #loans #mortgage #derivatives #VIX http://link.eu5.net/851j

Valuation of European and American Options #Derivative Pricing in #Python #risk #riskmanagement #TLT #option #quant #trading #VIX #volatility http://tech.harbourfronts.com//valuation-european-america/

Interest Rate Swap-Derivative Pricing in #Python #derivative #risk #riskmanagement #TLT #mortgage #quant http://tech.harbourfronts.com//interest-rate-swap-derivat/

CLO Slowdown Would Be Boon for Leveraged Loans Japanese investors, who helped lead so-called CLOs to record issuance in 2018, now face more regulatory scrutiny at home over billions of dollars in investments in the complex products. #SPX #mortgages #loan http://link.eu5.net/5dkl