Time value

The option premium is always greater than the intrinsic value. This extra money is for the risk which the option writer/seller is undertaking. This is called the Time value.

Time value is the amount the option trader is paying for a contract above its intrinsic value, with the belief that prior to expiration the contract value will increase because of a favourable change in the price of the underlying asset. The longer the length of time until the expiry of the contract, the greater the time value. So,

Time value = option premium – intrinsic value

Intrinsic value

The intrinsic value is the difference between the underlying spot price and the strike price, to the extent that this is in favor of the option holder. For a call option, the option is in-the-money if the underlying spot price is higher than the strike price; then the intrinsic value is the underlying price minus the strike price. For a put option, the option is in-the-money if the strike price is higher than the underlying spot price; then the intrinsic value is the strike price minus the underlying spot price. Otherwise the intrinsic value is zero.

For example, when a DJI call (bullish/long) option is 18,000 and the underlying DJI Index is priced at $18,050 then there is a $50 advantage even if the option were to expire today. This $50 is the intrinsic value of the option.

In summary, intrinsic value:

= current stock price – strike price (call option)
= strike price – current stock price (put option)

在期权交易中如何利用希腊值?

原文链接

Greeks值在实际应用中指代的意义

对于期权交易者而言,熟悉Delta、Gamma、Theta、Vega等的希腊值(Greeks值)的特征及性质是非常重要的,无论在交易策略制定上,还是在风险管理上。可以说,了解这些Greeks值在实际应用中指代的意义,以及如何在实际交易过程中加以应用,是一个合格交易员必须掌握的知识与技能。

1.1、Delta指代意义

Delta(Δ)代表标的标的物价格变动对看涨期权价格变动的敏感度,在实际应用过程中,该指标还具备以下功能。

(1)风险资产对冲计量的依据。如果Δ=0.22,出售1单位看涨期权需要买入22(=0.22×100)股的标的股来对冲风险。又例如,如果Δ=-0.6,出售1单位看跌期权需要卖出60股来对冲风险。

(2)在到期时看涨期权是实值的概率。如果Δ=0.6,该看涨期权到期时,成为实值的概率为60%,投资者有60%的机会获利(若其他情况不变)。

(3)风险警示界限。就限界期权(敲入或敲出期权)而言,当标的物价格接近限界(或关卡)时,其Delta经常超过1,也可能变为很大(比如Δ=3),这会被风险管理经理认为该期权的风险已是标的股的3倍,并要求交易员减仓,降低期权的风险。

另外,需要说明的是,虽然理论告诉我们,Delta对冲风险必须是连续性的进行。但在实务操作时,连续对冲将产生较高的交易费用,故需采用离散式的对冲(discrete hedging)风险。这样交易成本会下降,但同时对冲风险的效率也下降,故在实际过程中,需要在“对冲误差”、“交易成本”二者之间进行权衡与取舍。

1.2、Gamma指代意义

看涨期权的Gamma(Γ)是看涨期权价格的二阶导数(也是看涨期权Delta的一阶导数),该指标在实际应用过程中还具备以下指代作用:

(1)Delta敏感性因子。它代表了看涨期权价格曲线在给定价格点的曲率。它是Delta关于标的物价格变化的敏感性。Gamma越大,看涨期权价格越敏感,即表示该看涨期权在该给定标的物价格的风险越大。其中,平值期权的凸形风险最高,越是实值(或虚值)期权的凸形风险越低。此时,标的物价格变动对期权价格影响很小。所以,买入的期权处于平值附近时,当标的物价格上行的幅度较大时,投资者获利较多,而卖方则对应的亏损就较高。

(2)Delta-Gamma中性对冲因子。一方面,若要对冲Gamma风险,可以用另外的期权去对冲。例如,两个豆粕期货期权的GammaΓ1、GammaΓ2,二者存在这样的关系GammaΓ1/GammaΓ2=0.40/0.20=2。所以,要对冲第1个期权的Gamma风险,需要买(或卖)2手的第2个期权来对冲。另一方面,若只对冲Gamma风险会扭曲组合的Delta风险的对冲,所以在实际应用中,最好采用Delta-Gamma中性对冲方法。这就需要采用两种期权,并求解出一个二元方程的解,计算出两种期权的具体手数,这样才能做到对冲原来期权的Delta-Gamma风险。这种方法对冲效果较为理想,不过因采用两种期权对冲风险,其成本可能比较高。

1.3、Vega指代意义

Vega风险可以由每1%的波动率变化所引起的期权价格百分比的变化来衡量。在实际应用过程中,它还具备以下作用:

(1)波动率与期权价值之间纽带。布莱克-斯科尔斯定价模型假设的标的物价格波动率在期权有效期限内是固定的,但实际上波动率会随着标的物价格和时间而变化,当然也会因为宏观经济因素等外在因素的变动而造成波动率的变动。所以,Vega值帮助我们知道,当标的股波动率变动时,会造成期权价值多少百分比的变动。

(2)风险度量的因子。Vega代表的是期权价格随着标的股波动率变化而变化的敏感性。Vega越高,期权价格的变化越大,因此会导致由更高波动率变化所引起的更大的期权风险,即Vega风险。

1.4、Theta指代意义

时间衰减因子(time decay factor),是指随时间流逝期权价值的下降速度。在其他条件相同的情况下,Theta值通常表示为期权价值每日下降的点数。例如,在实际应用过程中,Theta值为0.05的期权的价值在其他市场条件不变时,每一天下降0.05。如果该期权今日价值为2.75,那么明天它将价值2.70,后天它将价值2.65。无论看涨期权或看跌期权,所有期权的价值都会因到期时间的临近而下降。

原文链接

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.

Credit Default Swap (CDS), Collateralized Debt Obligation(CDO)

CREDIT DEFAULT SWAPS (CDS)

This is a contract that provides insurance against the risk of a default by particular company. The company is known as the reference entity and a default by the company is known as a credit event.

The buyer of the insurance obtains the right to sell bonds issued by the company for their face value when a credit event occurs and the seller of the insurance agrees to buy the bonds for their face value when a credit event occurs. The total face value of the bonds that can be sold is known as the credit default swap’s notional principal.

An ABS where the underlying assets are bonds is known as a collateralized debt obligation, or CDO.

The precise rules underlying the waterfall are complicated, but they are designed to ensure that if one tranche is more senior than another it is more likely to receive promised interest payments and repayments of principal.

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

combination, straddle, strap, strip, strangle

A combination is an option trading strategy that involves taking a position in both calls and puts on the same stock. We will consider straddles, strips, straps, and strangles.

One popular combination is a straddle, which involves buying a European call and put with the same strike price and expiration date.

straddle

A strip consists of a long position in one European call and two European puts with the same strike price and expiration date.

A strap consists of a long position in two European calls and one European put with the same strike price and expiration date.

strap and strip

In a strangle, sometimes called a bottom vertical combination, an investor buys a European put and a European call with the same expiration date and different strike prices.

strangle