Greeks

 Delta

\Delta = \frac{\partial V}{\partial S}

Delta,\Delta , measures the rate of change of the theoretical option value with respect to changes in the underlying asset’s price. Delta is the first derivative of the value V of the option with respect to the underlying instrument’s price S.

Vega

\nu=\frac{\partial V}{\partial \sigma}

Vega measures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset.

Theta

\Theta = -\frac{\partial V}{\partial \tau}

Theta,\Theta , measures the sensitivity of the value of the derivative to the passage of time (see Option time value): the “time decay.”

Rho

\rho = \frac{\partial V}{\partial r}

Rho,\rho , measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term).

Lambda

\lambda = \frac{\partial V}{\partial S}\times\frac{S}{V}

Lambda,\lambda , omega,\Omega , or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.

Psi

{\displaystyle \psi ={\frac {\partial V}{\partial q}}}

Psi (Ψ) is the total change in option value over the total change in the underlying assets dividend rate, if the asset pays dividends.

Value at Risk (VaR)

Value at Risk (VaR) is an attempt to provide a single number summarizing the total risk in a portfolio of financial assets.

VaR实际上是要回答在概率给定情况下,银行投资组合价值在下一阶段最多可能损失多少。

VaR特点①可以用来简单明了表示市场风险的大小,单位是美元或其他货币,没有任何技术色彩,没有任何专业背景的投资者和管理者都可以通过VaR值对金融风险进行评判;②可以事前计算风险,不像以往风险管理的方法都是在事后衡量风险大小;③不仅能计算单个金融工具的风险。还能计算由多个金融工具组成的投资组合风险,这是传统金融风险管理所不能做到的。

但VAR方法也有其局限性。VaR方法衡量的主要是市场风险,如单纯依靠VaR方法,就会忽视其他种类的风险如信用风险。另外,从技术角度讲。VaR值表明的是一定置信度内的最大损失,但并不能绝对排除高于VaR值的损失发生的可能性。例如假设一天的99%置信度下的VaR=$1000万,仍会有1%的可能性会使损失超过1000万美元。这种情况一旦发生,给经营单位带来的后果就是灾难性的。所以在金融风险管理中,VaR方法并不能涵盖一切,仍需综合使用各种其他的定性、定量分析方法。

VaR按字面的解释就是“处于风险状态的价值”,即在一定置信水平和一定持有期内,某一金融工具或其组合在未来资产价格波动下所面临的最大损失额。

I am X percent certain there will not be a loss of more than V dollars in the next N days. The variable V is the VaR of the portfolio. It is a function of two parameters: the time horizon (N days) and the confidence level (X%). It is the loss level over N days that has a probability of only (100 – X)% of being exceeded. Bank regulators require banks to calculate VaR for market risk with N = 10 and X = 99

Volatility Smiles

Volatility Smiles

波动率微笑(Volatility smiles)指期权隐含波动率(implied volatility)与行权价格(strike price)之间的关系。

常规来说,Black-Scholes定价模型中假设股价波动率是常数,在实际中一般低估了标的物的波动率。对于股票期权来说,行权价格越高,波动率越小,当行权价趋于正无限时,看涨期权价格趋近于0,看跌趋近于正无限,波动率均趋近于0;而对于汇率期权来说,则行权价越接近现价,波动率越小。

而之所以被称为“波动率微笑”, 是指价外期权和价内期权(out of money和 in the money)的波动率高于在价期权(at the money)的波动率,使得波动率曲线呈现出中间低两边高的向上的半月形,也就是微笑的嘴形,叫波动率微笑。

out-of-the-money option

虚值期权,又称价外期权,是指不具有内涵价值的期权,即敲定价高于当时期货价格的看涨期权或敲定价低于当时期货价格的看跌期权。如果把企业的股权资本看作是一种买方期权,则标的资产即是企业的总资产,而企业的负债值可看作是期权合约上的约定价。期权的有效期即与负债的期限相同。

价内期权 In the Money,指执行价格与基础工具的现行远期市场价格相比较为有利的期权。

volatility smile1volatility smile2

Capital Asset Pricing Model (CAPM)

The capital asset pricing model (CAPM) is a model that can be used to calculate the expected return from an asset during a period in terms of the risk of the return. The risk in the return from an asset is divided into two parts. Systematic risk is risk related to the return from the market as a whole and cannot be diversified away. Nonsystematic risk is risk that is unique to the asset and can be diversified away by choosing a large portfolio of different assets. CAPM argues that the return should depend only on systematic risk.

CAPM

assumptions.

  1. Investors care only about the expected return and standard deviation of the return from an asset.
  2. The returns from two assets are correlated with each other only because of their correlation with the return from the market. This is equivalent to assuming that there is only one factor driving returns.
  3. Investors focus on returns over a single period and that period is the same for all investors.
  4. Investors can borrow and lend at the same risk-free rate.
  5. Tax does not influence investment decisions.
  6. All investors make the same estimates of expected returns, standard deviations of returns, and correlations between returns.