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9

It seems that you are thinking of the volatility as some sort of standard deviation of your stock price. It is not. In the BS model, $\sigma\sqrt{T}$ is the standard deviation of the log-return $\log(\frac{S_T}{S_0})$. There is no mathematical upper bound to its standard deviation. There is also no mathematical problem with returns being negative either. ...


3

This letter (if present) indicates which exchange(s) the option trades at, whereby: No hyphen or letter present = Composite A = AMEX American Stock Exchange B = BOX Boston Stock Exchange - Options E = CBOE Chicago Board Options Exchange I = BATS J = NASDAQ OMX BX O = NASDAQ OMX P = NYSE Arca X = PHLX ...


3

A very popular choice for mean reversion is the Ornstein–Uhlenbeck process (here in discretized form): $$L_{t+1}-L_t=\alpha(L^*-L_t)+\sigma\epsilon_t$$ Here you see that the level change is governed by some parameter $\alpha$, the mean reversion rate (or speed), and the distance between the long run mean $L^*$ and the actual level $L_t$ plus some noise. A ...


2

A Heat Rate Option is a standard contract traded bi-laterally or on an exchange where the ratio between Electricity at an agreed location and Natural Gas at an agreed location is the strike price for an agreed quantity at an agreed expiration date. This allows holder the ability to manage the the cost of the Market Implied Heat Rate. For example if May ...


2

Intuitive, no math explanation: Imagine two call options, option A expiring tomorrow and option B expiring in two months. Both of the options are way out of the money and have the same strike price. Due to some event the implied volatility of the stock spikes. Let's assume stock price stays the same. Does the chances of option A expiring in the money ...


2

The price of the April option will be more than $5.00, correct. How much more depends on the implied volatility ($\sigma$) of the option and the interest rates ($r$). The higher $\sigma$ and $r$ are, the higher the time value of money and the value of the April option. I highly recommend playing around with this calculator to gain an intuitive ...


1

Conversion to a butterfly can mitigate or even eliminate all risk taken by opening a initial debit spread or long option position. This is possible only if the underlying moved in your favor after your initial position is open. To convert to a butterfly you simply sell and buy enough options (for a credit) that together with your initial position forms a ...


1

By no arbitrage, $S(0)=(Su q+Sd (1-q))/(1+r)$ and $C(0)=((Su-k)^+ q+(Sd-k)^+(1-q))/(1+r)$. Simplifying and rearranging (and assuming $Su>k$), $$\left[\begin{array}{c} S(0) \\ C(0) \end{array} \right]=\frac{1}{1+r}\left[\begin{array}{cc} Su & Sd \\ (Su-k) & 0 \end{array} \right]\left[\begin{array}{c} q\\ 1-q \end{array} \right] $$ Clearly, ...


1

The answer of AFK is very good and accurate in a BS setting. Thinking of jumps I would add the following: If we assume that stocks sometimes move in jumps (usually downwards) then it is clear that ATM or OTM options shortly before expiration with a price that accounts for the possibility of a jump - which is therfore quite high - only fit in the BS ...


1

If someone wants simple intuition, here is what happened to the drift. It did go into the formula, believe it or not, but it came into the B-S math sort of in two ways so it cancelled out in the end. It disappears because Black-Scholes assumes people may have different preferences for risk, but at least everyone is consistent on their own preference. ...



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