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7

You could also look at how each price level is made up. For example how is the 18 lot on the bid price 0.0995 collated. Is it a 5 lots, 5 lots, 7 lots and 1 lot. You can do this on certain exchanges as they have an enhanced order book where you can see every insert, modification, delete and trade. This may require you to recreate the order book, which ...


6

In practice, things are actually quite different and a bit more subtle. You really need to differentiate between the underlying being an index or e.g. a single stock. I will try to provide some insight: Index options are, in general, of European type. The market quotes prices for calls and puts and you can back out the implied vols via the usual BS formula. ...


5

Implied Volatility (IV) is determined from the price of options, which you can think of as an insurance on the underlying stocks. So, if investors think there is a large change of big moves, they will pay more to buy and charge more to sell options, so price and IV go up. There are many factors that influence IV. Some of the major ones are: Spot-Vol ...


5

Note: what you call true volatility is often termed realized volatility. When you purchase a call or a put, each time the underlying increases in value, your hedge modification consists of selling a little bit. When it drops in value, you buy a little bit. Those buy-low/sell-high elements are a replication strategy that, as you note, would be expected to ...


5

Further notes: One shouldn't build an implied volatility surface just from call prices or just from put prices. One should build it from liquid instrument quotes and, if necessary, some less liquid ones. Some markets, like FX option one, quote package prices (butterfly, risk reversal, ATM straddles). Deciding how to parameterize the implied volatility ...


4

Call and a put of the same strike have the same I.V, in theory. The ONLY reason for this to differ is the limits to arbitrage on call put parity. Now this is a static strategy that has no rebalancing - so the only problem here is transaction costs in buying/shorting the stock. So if you have reason to believe that this strategy is difficult to implement, ...


4

He circled the volume of the option in question. It was roughly 50,000 and one option contract is usually for 100 shares. Price was 0.13. $50k*100*0.13 = 650k$


4

I will assume that you have a set of "sheets" like a market maker. I.e different calendar terms of theoretical prices that your model has spat out. Lets say: July Straddle = 100 October Straddle = 150 If someone sells the July-Oct Put Calendar, selling Oct, Buying July for 20. If the theoretical value on our sheets is 22. Then that means we have ...


4

Implied volatility is calculated from the price of the option contract, not the stock price. Thus, it is influenced by the "supply & demand" of the options. There are scenarios where the stock price remains flat while the IV of options change, examples include approaching expiration of the option, earnings reports, etc.


4

SPY pays dividends ~1.8%, and the expiry is ~3y (as of date was 2018, 2021 expiry), so the it looks like there is a discount Assuming $0 time value $$OptionValue=Intrinsic Value+Time Value $$ $$OptionValue= (S-K)-Dividend$$ $$OptionValue=267x(1-0.02)-267x1.8\%x3=\\\$247$$


3

Consider a financial market with a filtered probability space $\left(\Omega,\mathcal{F},(\mathcal{F}_t),\mathbb P\right)$ satisfying usual conditions equipped with a stock price process $S_t$. Suppose there exists a risk-free asset who is governed by $\mathrm{d}B_t=r_tB_t\mathrm{d}t$. Suppose the market is free of arbitrage, i.e. there exists a probability ...


3

In Black Scholes $$\frac{dS}{S}=rdt+\sigma dW$$ $dC_{BS}(S,t)=\underbrace{\frac{\partial C_{BS}}{\partial t}dt}_{Theta PnL}+\underbrace{\frac{\partial C_{BS}}{\partial S}dS}_{DeltaPnL}+\underbrace{\frac{1}{2}\frac{\partial^2 C_{BS}}{\partial S^2}dS^2}_{GammaPnL}$ $dC_{BS}(S,t)=\frac{\partial C_{BS}}{\partial t}dt+\frac{\partial C_{BS}}{\partial S}dS+\frac{...


3

This is a forward starting option. It's price cannot be determined by the vanillas you have because vanillas only determine the marginal distributions of the random variables - whereas to price this one, you need to somehow produce a joint distribution (correlate $X_{T1}$ and $X_{T2}$). An equivalent way of doing the same thing is the following. You need to ...


3

No Because the P&L it generates is in $O(dt^2)$. Ito's lemma tells you that you can ignore this P&L. $$PnL = \frac{\partial^2 V}{\partial t^2}dt^2 = 0$$


3

Following this answer, let $\mathbb Q$ be the probability measure associated to the risk-free bank account as numeraire and $\mathbb Q^1$ the probability measure associated to the stock as numeraire. You know that the standard equation $\mathrm{d}S_t=rS_t\mathrm{d}t+\sigma S_t\mathrm{d}W_t^\mathbb{Q}$ can be written as $\mathrm{d}S_t=(r+\sigma^2)S_t\mathrm{d}...


3

As @ir7 did, I only briefly want to add to @noob2's spot-on answer. He's of course right and $\Lambda=\Delta\frac{S}{V}$ decides how risky the option is compared to the stock. Firstly, note that $\Lambda=\frac{\frac{\partial V}{V}}{\frac{\partial S}{S}}=\frac{\partial V}{\partial S}\frac{S}{V}$. An economist would call $\Lambda$ an elasticity. It tells you ...


2

Consider a vanilla european option. The optimal strategy in the risk neutral measure is to exercise if $S(T)>K$. (because in the risk neutral world, I value my payoff at its expectation, which at that point is the payoff itself. At time T, if $S(T)-K$ is positive, I will take it over not exercising, which is a payoff of 0. This is of course also optimal ...


2

Let $C=(S-K)^+$ and $P=(K-S)^+$. Then it is clear, for any positive integers $i$ and $j$, \begin{align*} C^i P^j = 0. \end{align*} Consequently, for any positive integer $n$, \begin{align*} (C+P)^n = C^n + P^n. \end{align*} Your conclusion now follows immediately.


2

The implied volatility is not G_d given, but comes from the collective judgement of market participants. If you are right and the market is wrong (unlikely in my personal experience but perhaps true for you) then you can make money when you are proven right by future developments (i.e. by future realized volatility being close to your prediction and higher ...


2

In my experience this is not easily hedgeable. Expected volume can be hedged using baseload futures, or, if you are in a very liquid market (Germany) a combination of baseload and peak. You will still be exposed to the intraday shape, and, in the long term (you can hedge the first months and quarters but at some point you need to resort to calendar products) ...


2

Put-Call Parity says that \begin{align} C - P = D(F-K) \end{align} where $C$ and $P$ are the prices of two options at the same strike, $D$ is the discount factor to expiry (probably very close to $1$ right now...), $K$ is the strike and $F$ is the forward price, which you're trading via futures. This is a model independent result, if it doesn't hold then you ...


2

Does shorting DOOM puts yield consistent return? Yes*. (I'll get to that star shortly.) Is there a crash risk premium built into those puts? Yes. Are there papers studying these? Yes; many. Bondarenko (2014) is by far the go-to paper on this topic. In fact, you will see many citations of the paper throughout the expensive put options literature, even before ...


2

You may be looking for synthetic longs/shorts which would be buying/selling an ATM call and selling/buying an ATM put. This will give you leverage while nearly replicating the underlying. I would caution that if you're only looking to hold for a couple hours, you will need to seriously consider the transaction costs.


2

It is just whatever the option is worth assuming the underlying is currently trading at the reference rate and assuming the option carries the amount of deltas the brokers says it has. Usually there is some negotiating on what the fair delta is - since different people use different models/assumptions and have different deltas. If the delta is different ...


2

An example of volatility trading would be constructing pure long/short volatility positions by buying/selling strangles (OTM calls and puts) and then delta hedging the position with the underlying.


1

This looks similar to a cliquet or "ratchet" option: an option with a strike price which resets occasionally. The Wikipedia definition of a cliquet is a bit too restrictive since one of the most common uses of such options was by Japanese firms which issued warrants and convertible bonds in the 1990s after the implosion of the Japanese real estate ...


1

When you replicate the option, you negatively scalp yourself when hedging deltas (if you are short the option). That negative scalp should be offset by theta you make by being short the option, and thus on net your option + hedge has 0 pnl. This obviously assumes realized volatility = implied volatility. If your option has high IV but underlying doesn't ...


1

I suspect that the reference value is, well, only for reference and not the real price. Maybe the price of SPY when the call contract is bought is lower


1

Here is an answer from a statistical angle: Your hedged VIX corresponds to a regression residual. If you estimate the regression by OLS, the residual will by construction be uncorrelated with stock returns. The two plots look similar because of a constant trend in stock prices that does not affect the correlation between returns and the VIX. If you do not ...


1

You have not achieved replication here. The idea is that, tomorrow, I must end up with portfolio value equal to the value of the option. That is not guaranteed with this setup. To see that, try to write $dV(t,S(t))$ from Ito's lemma and from your equation, see if they match.


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