Greeks

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 of the option with respect to the underlying instrument’s price .

Vega

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

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,, 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,, 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

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。

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

out-of-the-money option

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.

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.

Hedge ratio

The hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure. When the asset underlying the futures contract is the same as the asset being hedged, it is natural to use a hedge ratio of 1.0.

hedgers, speculators, and arbitrageurs

Three broad categories of traders can be identiﬁed: hedgers, speculators, and arbitrageurs.

Hedgers use derivatives to reduce the risk that they face from potential future movements in a market variable.

Speculators use them to bet on the future direction of a market variable.

Arbitrageurs take oﬀsetting positions in two or more instruments to lock in a proﬁt.