# Dynamic Asset Pricing

*Dynamic Asset Pricing* [edit]

Dynamic Asset Pricing^{[1]} is an economic approach that incorporates portfolio selection and the theory of asset pricing in a setting that has multiple periods and uncertainty. Dynamic asset pricing combines risk management practices used to manage uncertainties and asset pricing theories to allocate prices to assets in a continuous manner. Therefore, dynamic asset pricing focuses on maximizing the profitability of a portfolio by identifying and evaluating how different economic and market conditions affect the price of assets. The theory implies that asset prices cannot be fixed long enough before a change occurs. There needs to be a flexible approach that addresses all the fluctuations within a market. Therefore, the application of economic principles and theories to understand the direction of an asset price helps in determining the current price of an asset. Dynamic asset pricing tends to flow with changes and fluctuations in the market to deal with risks of uncertainty and different macroeconomic and microeconomic factors affecting prices, demand, and supply. Asset pricing could be seen as a narrow application of economic theories to determine the price of assets without much changes to the decisions.

**Asset pricing theory**^{[2]}[edit]

Asset pricing is a combination of two main principles, general equilibrium asset pricing and rational pricing, out of which many models have been developed.Dynamic asset pricing theory is an extension to the normal asset pricing theory.

**General equilibrium asset pricing** [edit]

This principle describes how market prices are determined by supply and demand. This approach is used when evaluating a diverse portfolio, whereby one asset price is spread across many assets. The quantity of the assets supplied and the quantities of the assets demanded should be equal at a specific price (Cochrane, 2009). The price of assets at any given time reflect the true value of those assets. General equilibrium asset pricing reflects the risk associated with the cash flows in a portfolio. General equilibrium asset pricing focuses on providing insight about the price of an asset in relation to other assets, and this helps to identify assets whose cash flow is sufficient enough to prevent any sudden changes to prices. The general equilibrium theory brings market prices to a balance where the consumer pays for a realistic price instead of an exaggerated price.

**Rational pricing**[edit]

Under relational pricing, the prices of derivatives are determined in a way that they are arbitrage free. Arbitrage-free is a situation where traders cannot take advantage of the difference in asset prices by buying and selling assets simultaneously to make a profit from the difference in prices in different markets. Relational prices focus on individual assets by determining the fixed incomes or bonds that have one asset (Cochrane, 2009). Unlike the general equilibrium theory, rational pricing seeks to create a unique risk price for every asset. Creating unique prices for an asset implies that traders cannot take advantage of difference in prices between markets in order to make profits. The price is stabilized at a price that reflects in all the markets, and this helps to avoid incurring losses due to disjointed prices. In the case of general equilibrium theory, where the risk of investing is spread across a diverse portfolio, an investor looks at long term results and goal. However, rational pricing bring more attention to the stability of prices by evaluating the current value of an asset, relative to the demand, in order to determine one price across markets.

**State pricing** ^{[3]} [edit]

State pricing refers to a contract where a party agrees to a contract of paying for an asset when a particular state occurs at a given time, without which no payment is made. The probability of asset prices and the preference of agents determine the state price (Kercheval, 2012). State pricing only happens when there are two underlying parties with complementary interests: one has the desire to buy with the aim of making a profit while the other also has the desire to sell with the aim of making a profit. Therefore, both sides of the trade agree on a specific price when both of them will be willing to buy and sell respectively. However, when the price does not hit the targeted expected, the contract between the two parties will not be executed. Additionally, the state expected at any given time could be something else other than price. Certain economic events could also trigger the execution of a contract between a seller and a buyer. State pricing usually varies from asset to asset, but it helps protects investors because the approach allows traders to determine the conditions when an asset will be profitable.

# **Portfolio Selection**[edit]

a. **A structural model** is a term that is used in investment to refer to the selection of diverse securities that are to be included in a portfolio. The value and volatility of the assets are factors that are considered when selecting assets for a portfolio. The process of managing assets should be determined per the market that is targeted (Derbali, 2018^{[4]}). The liabilities of any given portfolio must be identified as this helps reduce any risks associated with a portfolio. Value and volatility are used to determine the potential risks and opportunities that an asset presents. The value of one unit of an asset determines how much profit a trader makes from an investment. Traders rely on volatility of prices in order to make profits, but if the variance in prices is too unpredictable and fast, then there is a risk of losing a lot of money within a few minutes or seconds. Investors prefer asset prices that are volatile enough to allow them to make profits. But it is also vital that investors and traders understand what they stand to lose if the trade does not yield as expected, which is why strategies such as hedging help reduce risk by taking offsetting positions.

b. **Derivative valuation**. A derivative is a contract that specifies the obligation to receive or deliver future cash flows based on a future event. Therefore, two parties can agree to sell and buy an asset respectively when a certain event has occurred. Discounted cash flow^{[5]} (DCF) is a formula that is used to determine the value of derivatives based on future cash flows. The sum of future cash flows is used to determine the net present value (NPV) of a derivative (Discounted cash flow). Derivatives are used in speculating, hedging, accessing remote markets, and distributing risks as securities.

c. **Hedging**^{[6]} **methods.**

Hedging is an approach where the risk of adverse price movements of an asset is reduced by investing in offsetting positions. A hedge can be constructed for different types of financial instruments like a futures contract, stocks, insurance, swaps, and gambles. There are three types of hedging: back-to-back, tracker, and delta hedging. Back-to-back hedging is a strategy where all open positions are immediately closed (Clark & Ghosh, 2004). The alternative of closing all positions eliminates any risk of incurring a loss, but it could hinder investors from realizing long term profits. Tracker hedging is where an open position is decreased as the maturity date gets closer (Clark & Ghosh, 2004). With the tracker hedging approach, traders can target to make long term profits by reducing the amount of their investments. Reducing the size of a portfolio will reduce the risk of losing big while presenting an opportunity to make profits in the future. Delta hedging mitigates financial risks by taking offsetting positions in other assets based on price changes (Clark & Ghosh, 2004). The delta hedging approach is relevant where the price of an asset moves against expectations and it will be a loss if the position is closed. Therefore, hedging is used to protect a portfolio from different financial risks such as commodity risk, credit risk, interest risk, currency risk, equity risk, volume risk, and volatility risk.

d. **Dynamic programming.**^{[7]}

Dynamic programming is a recursive method used to solve sequential decision problems in both discrete and continuous time settings. Dynamic programming has three components: optimization, integration, and approximation (Cai, 2009). In a continuous time model, where there is no closed-form solution, approximation is the most commonly used method. Approximation is done by using the discrete time version to break the continuous time into small successive intervals that can be used to make decisions at any given time (Cai, 2009). Dynamic programming draws its principles from mathematics, statistics, and other fields in order to make informed decisions, especially when highly valuable and volatile assets are involved. There are different factors that affect the volatility and value of asset prices, and traders need to be aware of the potential risks at all times before making decisions. Furthermore, some asset prices require consistent adjustment as per the market volatility to protect a trader’s position.

# **Uncertainty and Risk**[edit]

Any investment carries with it certain risks because prices are always changing and they are subject to volatility due to factors like politics, economic decisions, and market demand. Therefore, there is always uncertainty and risk in any given asset, which is the pricing of assets should be done systematically to optimize profitability and minimize potential loses. Inasmuch as it is impossible to determine all the potential risks and opportunities of an asset, there are approaches that help minimize human error.

a. **Systemic risk**^{[8]}Systemic risk refers to the complete failure of a company or an investment portfolio (Peterson, 2012). Factors such as volatility and value and approaches such as hedging and dynamic programming are critical in developing a diverse investment portfolio that has no single point of failure. For instance, if an investor bought different assets in one type of financial market, then, in the event of market failure, the entire portfolio will be at risk of incurring massive losses. The characteristics of an asset in terms of its value and volatility should be different within a portfolio, which helps to spread the risk. Investing in assets blindly without evaluating their correlations could see a portfolio cleaned out when the market conditions are not favorable.

b. **Capital asset pricing model (CAPM)**^{[9]}**.** CAPM is a model used to theoretically determine the appropriate rate of return of an investment to make decisions concerning adding assets to a diversified portfolio (Fama & French, 2004). The CAPM is used to price individual security or portfolio due to its simplicity and application in different situations. Using CAPM, traders can determine if a particular assets profit potential is within their risk tolerance levels.

c. **Arbitrage pricing model.** Arbitrage is the process of capitalizing on price differences between two or more markets to make a profit. An arbitrage opportunity is inherent when something can be instantaneously bought at a low price and sold at a higher price (Qian, 2019). An arbitrage is risk-free because traders are only involved in taking advantage of price differences by buying and selling for profit. However, the market always carries some uncertainty, which is several arbitrage models have been developed to manage risks such as volatility of prices. There might be differences in prices between markets but traders also need to determine the stability of the price variations. Losses can be incurred if the price of an asset fluctuates faster.

d. **Martingale pricing**^{[10]}**.** Martingale is a probability theory that uses a sequence of random variables to determine the price of an asset at a particular time when it will be equal to the present value (Pascucci, 2011). Martingale approach uses mathematical formulae, in both discrete and continuous time, to determine the best time to invest in an asset with the expectation that the future price will reflect the current price.

e. **Stochastic volatility**^{[11]}. Stochastic volatility assumes that the volatility of asset prices is never constant, and this problem is corrected using the Black Scholes model that lets the volatility to vary over time (Kahl, 2008). Stochastic refers to a variable that is determined randomly and is not easy to predict with precision. A security's volatility is considered a random process that is governed by state variables such as the variance of volatility and the price level. Understanding an assets volatility provides better insight when selecting assets for a portfolio.

**Reference**

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- ↑ "Asset pricing",
*Wikipedia*, 2019-05-16, retrieved 2019-05-16 - ↑ Qian, J. Introduction to Asset Pricing Theory, 2019. Retrieved from, http://jhqian.org/apt/apbook.pdf
- ↑ "State prices",
*Wikipedia*, 2018-04-25, retrieved 2019-05-16 - ↑ https://hal.archives-ouvertes.fr/hal-01696009/document
- ↑ "Discounted cash flow",
*Wikipedia*, 2019-05-16, retrieved 2019-05-16 - ↑ "Hedge (finance)",
*Wikipedia*, 2019-05-07, retrieved 2019-05-16 - ↑ https://stacks.stanford.edu/file/druid:zd335yg6884/YongyangCai_thesis-augmented.pdf
- ↑ "Systemic risk",
*Wikipedia*, 2019-03-02, retrieved 2019-05-16 - ↑ "Capital asset pricing model",
*Wikipedia*, 2019-04-23, retrieved 2019-05-16 - ↑ "Martingale pricing",
*Wikipedia*, 2019-02-21, retrieved 2019-05-16 - ↑ "Stochastic volatility",
*Wikipedia*, 2019-05-06, retrieved 2019-05-16