# Tag Info

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In my opinion, professionals mainly trade options if they want to trade the volatility. I believe there is a mathematical proof that shows that if the realized underlying volatility between the option ...
• 6,223
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### Positive theta on a long put?

If a european option value becomes lower than intrinsic value it gets negative time value. In this circumstance the theta becomes positive because as time approaches to expiry the option value has to ...
• 2,197

In addition to other reasons mentioned here, options tend to be expensive to trade (they have high bid-ask spreads). These do add up in institutional asset management, so best avoided. Further, if ...
• 191

So, from this simple no-arbitrage argument, we see that the price of the option must always be at least its intrisic value. Yes indeed However, at this point I realized something strange: if this ...
• 14.7k
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### Can an In-the-Money Put Option's price $>$ its Strike Price?

Under the assumption that the underlying cannot have a negative value, then the value of a put option cannot be greater than the strike. The reason behind this doesn't require maths, it's fairly ...
• 2,581
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### Given $\mathbb{E}[X]$, $\mathbb{E}[\max(0,X)]$, and $\mathbb{E}[\min(0,X)]$, what is $\mathbb{E}[f(X)]$

I don't think one can answer your question. Suppose $X=e^{\mu+\sigma Z}$ is log-normal, i.e. positive. Thus, $\mathbb{E}[\max\{0,X\}]=\mathbb{E}[X]$ and $\mathbb{E}[\min\{0,X\}]=0$. From just knowing ...
• 16.1k

### Can increase in volatility reduce the price of a deeply in-the-money European put?

If you hold an option, you're always vega long, i.e. if volatility increases, your position increases as well - regardless of moneyness and the option type (put or call). Note firstly that by the ...
• 16.1k
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### How to create a synthetic put?

As you can see from the wiki page, the delta of a put is $$\Delta = -e^{-qT}N(-d_1)= -e^{-qT} \left(1-N(d_1)\right)$$ Recall that this $\Delta$ is the derivative of the value of the put $p$ with ...
• 11.2k
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### When does the CBOE Put Protection Index (PPUT) make profit?

The PPUT strategy is an example of a "tail protection strategy". The objective is to have a return somewhat similar to the return of the S&P 500 but with better performance during "crashes" (sharp ...
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### Delta Hedging/ Exchange for Currency Options

I am assuming you are short EUR and long USD based on your description of your hedges. I am also assuming the size of your hedges and your fx position are the same. In the first example of a hedge ...
• 6,652
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### How to Take Advantage of Arbitrage Opportunity of Two Options

I think it is far easier to understand by just drawing the payoffs. You have two put options: A European put option on a non-dividend paying stock with strike price 80 is priced at 8 dollars, and a ...

Puts are not available on all names, or might only be available for a limited set of expiries. I'm sure there are other reasons but those are the two most obvious.
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At the risk of making maybe three obvious points: 1- Many funds' investment theses are not predicated on a particular price point on a specific expiry date. They simply believe that X is too high ...
• 5,081
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### Most profitable PUT strike price in these times of high volatility?

You need an implied volatility assumption in addition to the price drop assumption to compute that. With a higher implied volatility increase the "profitability peak" you have will gravitate towards ...
• 2,908

### Kingdom of Denmark Nikkei put warrants

I assume you are referring to the sentence in italics (italicization belongs to me) in the following paragraph on pp. 218-219 in Derman's book "My Life as a Quant". Though no one used that ...
• 1,046
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### is relating bounds to relation between time to maturity and european put option price correct?

There is no contradiction at all here. $Ke^{-rT}$ goes to zero for $T$ going to $\infty$ so the relation you mention suggests that $-S\leq p \leq 0$ as $T$ gets bigger. If $r>0$. Put prices can (in ...
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I think the chain of logic should be as follows: We have put value >= intrinsic. Therefore either put value > intrinsic or put value= intrinsic. If put value > intrinsic, then it is not optimal to ...
• 17.4k
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### Understanding the relationship between the Black-Scholes formula and a replicating portfolio

It is my understanding that a replicating portfolio for a put involves short selling stock and lending money. You cannot statically replicate an option. So this is not true in general, you'll need to ...
• 14.7k
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### Put call parity in practice

While this question is basic, I am answering because putting models and/or formulae into practice is a part of quant finance that is not covered extensively on this (or any other) SE. (The below will ...
• 4,348

### Put Volatility Smiles and Implied Volatility

This can be due to various effects. I will list you 2 of them off the top of my head: Jumps/Crashes : assume you were to price a put option which expires in a few days from now. Your diffusion model ...
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### Why does black scholes model give lower prices for puts with further time to expiry?

It's the interest rate component. That is more meaningful in the formula. Note that the call becomes more expensive. Think about it this way. You could buy the call and sell the put instead of ...
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Cost. And greed. They want to squeeze every penny that is possible out of their transaction. It costs much less, maybe nothing, to short stocks that do not even exist. However the risk is ...
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Two main reasons: cost/premium: there is upfront premium associated with purchase of any put option. If your option ends up out of money, your premium is lost. for example, if stock price remains ...
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### Put Volatility Smiles and Implied Volatility

The short answer: Your observation is caused by some sort of central limit theorem. The long answer: The reason for the volatility smile/skew is the non-normality of the assumed return distribution. ...
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### Use of cash delta vs forward delta and the mirror image rule

Forward delta is the option's sensitivity to the PV of a forward contract on the same underlying with same maturity as the option. It is a convention often used in FX markets (see for instance On a FX ...
• 5,682
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### Pricing perpetual American put option when interest rate is equal to 0

The PDE doesn't equal zero when I replace with the expression of $V(S)$ you gave. Threre is an issue in your PDE's the boundary conditions and its solution. Let's start with the regular american put ...
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### What is The Closed-Form Implied Volatility Estimator (As Defined by Hallerbach 2004) for A Put Option?

I would look to these papers below by Dan Stefanica et al. Very easy to code and yields better results. An Explicit Implied Volatility Formula Tighter Bounds for Implied Volatility

### Can increase in volatility reduce the price of a deeply in-the-money European put?

I just want to add a simple piece to this reasoning, that is very intuitive and not excessively mathematic, since the mathematic explanation has already been given in the other answers (I like to base ...
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I firstly fill in the gaps from Slade whose comments outline the answer and then I provide an alternative approach. Let $K_1\leq K_2$. You want to prove $P(S_t,K_1,T)\leq P(S_t,K_2,T)$. Recall ...