# 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？

Greeks值在实际应用中指代的意义

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。

1.2、Gamma指代意义

（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

# 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.

# 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

out-of-the-money option

# 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.

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.

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.