New answers tagged

-2

Recently because of some personal reason, I tried to price Snowball Autocall using MC and PDE, assuming single underlying. 12 months Snowball, Monthly autocall observations, Daily Put Down & In. Payoff: if Autocall, then 100% principal + autocall coupon if Knock in and No Autocall, then client lose because of short put if No autocall and No Knock in, ...


2

Good question! The answer to this is no. Let us work through a simple example to see why. Assume that the Gamma is $10$ and that the break-even move is $1$. For simplicity, also assume that, these are unchanged by price moves in the underlying (this is reasonably accurate for small price moves), so: $\Gamma = 10$ $\delta S_{Break-Even} = 1$ Note that we ...


0

In general I agree with the upvoted answers given above. But keep in mind that it is difficult to identify firms that are exclusive sellers of options, generally a market making firm has a complex (and ever changing) portfolio that includes both short and long positions. An "option seller" is an idealized construct that may not exist in real life. (...


0

A theoretical answer to your question is provided by Black-Scholes but remember that actual option prices are set by supply and demand (with guidance from models for different market participants.) You could also try to fit a model to the actual data to solve this problem, though that would be a much more complex (and costly) solution.


3

It's not just a question of buyers vs. sellers, but also of investors vs. market makers. Market makers (market making firms, or banks - for whom this holds doubly due to regulation) are out to earn the bid-ask spread in exchange for providing liquidity, this means their goal is to fill your trade and exit the risk they take by being on the other side of your ...


2

Hedging is more essential for an option seller, because without hedging, their potential loss is unlimited (for a short call) or practically unlimited (for a short put). So, even if the trader is deliberately taking a delta or gamma position, some hedging is likely. On the other hand, an option buyer may have no need to hedge if they are taking a directional ...


8

Your question comes at this correctly, in my opinion. There is indeed a buyer and a seller behind every option; but the hedging behaviour of the two need not be equivalent... I used to work in an investment bank, and we used to call this (politely) "pin risk", or (less politely) "the gamma hammer". The idea (not perfect, but close enough) ...


2

You shouldn’t only consider the speculative investor. Insurers are a great example. They buy options to hedge risks they have already sold in terms of variable annuities and fixed index annuities, amongst others. Pension plans also can buy options to hedge risks they’ve already promised. In this case, the option is a hedge asset, not a speculative asset. The ...


1

Just expand the term: \begin{align} \mathrm{E}(S_T) &= pS_o u + (1 - p)S_0 d \\ &= pS_o u - pS_0 d + S_0 d \\ &= pS_o (u - d) + S_0 d \end{align}


2

Old and golden question, and maybe a new perspective: As the previous answers have pointed out, distinction needs to made between "skewness" and "skew". The former is the third moment of returns, and the latter is what volatility traders/portfolio managers usually associate with the difference between two implied volatilities straddling ...


-1

The expected stock price move post an event is the expected return of the stock price right before the event. Therefore, using ATM option IVs in the formula gives the expected return based on current stock price. If Using OTM/ITM option IVs, I think the formula gives the expected return based on the OTM/ITM option strike price. Theoretically, for stock ...


5

I answer from a general discrete time/discrete state model point of view. This includes the binomial tree model as a special case. In finite dimensions, you can interpret asset payoffs and returns as vectors and retreat to linear algebra. Suppose you have $N$ states of nature and $J$ assets. Your payoff matrix is \begin{align*} A=\begin{pmatrix} X_1(\omega_1)...


1

Numéraire Change The time-$t$ price of a zero-coupon bond maturing at time $T$ is $$P(t,T)=\mathbb{E}^\mathbb{Q}_t\left[\exp\left(-\int_t^T r_s\text{d}s\right)\right].$$ Let $\mathbb{Q}$ be our standard risk-neutral probability measure which uses a locally risk-free bank account, $\text dB_t=r_tB_t\text dt$, as numéraire. From Geman et al. (1995), we know \...


0

Axibase Time Series Database is a non-relational alternative with a built-in schema for tick, EOD, and reference data. Querying statistics in ATSD by common criteria such as symbol, date range, strike price etc. should be much faster than reading from the input files since the order of records in files is not guaranteed and one generally needs to read the ...


0

The building blocks of this BRC are (assuming the most common specification, there is always variations but it's impossible to tell the details without any termsheet provided): long a zero-coupon bond short a down-and-in rainbow put on the min (worst-of), with barrier below strike usually, and either European or American exercise style The discount of the ...


2

Perhaps worthy of distinction is that a bank swap dealer would be a bilateral counterparty for an OTC uncleared derivative, but most options trade through broker-dealers and are centrally cleared (OCC, not the Fed). Retail trades would not go through the bank; they would trade through a broker who has an account with the OCC and must maintain certain excess ...


2

There are two forms of liability with options. The margin and the actual final settlement. Every day the options are evaluated to see their value. As the options fluctuate in value one counterparty will need to post more collateral and the other side will receive the collateral. In the case of OTC options the collateral may go to a neutral 3rd party. ...


4

Yes. Deposits with the Federal Reserve are assets owned by bank A. Typically they are rebalanced everyday. So: Day 1: Bank A deposits $ 1bn with FED. Day 2: Bank A receives back $1bn, pays $100mm to another CP and deposits $900mm with FED. Providing the bank operates within official regulations what it does with its $1bn is its own business, i.e. one such ...


0

I know this is perhaps the type of answer you seek, but there are alternative hedging products such as PPAs which could help with this. PPAs can be structured in many ways to allow for parties involved to be happy with the outcome. An as-produced PPA would probably solve your above issue. However, the outcome from a discussion regarding pricing would ...


2

I hope it's clear that implied volatilities cannot and should not be interpreted as estimates of future stock price volatility -- apart from anything else, every strike will have a different implied volatility, whereas there is only one value for the expected realized volatility. That still leaves the question of why the near-term out of the money put has ...


3

as it was stated correctly in the question all long butterfly options have to have a non-negative premium in order for No-arbitrage to hold. So we can say that: No-Arbitrage holds implies All Butterfly spreads have a non-negative premium. However, the reverse is not true. Just because all butterfly spreads have non-negative premiums does not mean that ...


0

"why do 1 DTE options have 80% IV at say 320 strike on spy when spy is at $386" 80% IV is simply the vol consistent with the option price and other inputs. One to look at it is sellers don't want to sell wings too cheap hence high vol on very short-dated options. "a movement of 80% or $308 per share over a 12 month period is equal to one ...


4

I am not sure why the question you link to does not provide an answer. I’ll try to answer it but it is really similar to what has already been said there. Bottom line is: if the value $K$ is reachable by the underlying asset $S$, that is $K$ belongs to the domain of process $S$, then the butterfly should be strictly positive. First note that the butterfly is ...


1

In the option pricing framework, one starts with a model for the underlying stock. In the Black-Scholes model, the stock price follows a geometric Brownian motion $$dS(t)=S(t)(\mu dt+\sigma dW(t))$$ where $\mu$ and $\sigma$ are two input parameters. From here, we can derive the price of, for example, a call option, and it turns out that the price of a call ...


1

When you market-make anything, you definitely take liquidity into account via the bid-offer spread (and via Implied Vol when you quote options). So if the underlying that you need to hedge with is not liquid like GME, the bid-off spread on the option will be larger than on options that have liquid underlying. Also the premium of the option (expressed as ...


4

Drifts under $\mathbb{Q}$ and $\mathbb{P}$ Some good answers already. Let me just repeat for clarity: under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates, i.e. typically this is the risk-free rate $r$ of the money market. The reason for this is the "no-arbitrage" argument: ...


1

Short answer, there are no studies on this. And any that claim to do this should not be trusted, because they can be negatively helpful ;-( The majority of option business is not conducted over any exchange, but OTC. It's a private transaction between the bank and the client. For every call or put you see in the "call-put ratio" publicised in much ...


2

There is a fascinating book from 1904 (yes, published more than 100 years ago) written by S. A. Nelson called "The A B C of Options and Arbitrage" (a reprint of it used to be available on Amazon here, for example) Quoting from that book: A CALL gives the owner and holder the right to call upon and buy from the writer of the privilege a certain ...


0

What suits you will depend much on your requirements, such as how fast does the db have to be, and the type of your analysis, e.g. whether you care more about the cross-section or time-series. I regularly store EOD option prices in CSV files (one file per option time-series), and then aggregate them as needed. I've written a small R package for that (https://...


0

Before the name was adopted in finance, the Optio was the deputy officer, the second in command after Centurion, in the Roman legion of imperial times. Not sure if he was allowed to carry fasci, but the man was chosen by the centurion, so perhaps this made it appealing for finance.


-1

Let's swap the word "call" with "359" and the word "put" with "22190". All the explanations here would make just as much sense using these replacement "words". The words "put" and "call" are so far removed from a rational meaning as to be meaningless, and even distracting. I know what a ...


1

Under your hypotheses, the implied volatility at which you close the trade out will be the forward volatility $\sigma_3$ where $\sigma_3<\sigma_2$, so you will make a loss on that. This loss will offset the theoretical gains you have made for the first 15 days of gamma hedging.


0

I think the author is just saying that \begin{equation} \begin{split} \frac{S - e^{-r}S_d}{S_u - S_d} S_u + \frac{e^{-r}S_u - S}{S_u - S_d} S_d &= \frac{S S_u - e^{-r}S_d S_u + e^{-r}S_uS_d - SS_d}{S_u - S_d} \\ &= \frac{S (S_u - S_d)}{S_u - S_d} \\ &= S \end{split} \end{equation} and that \begin{equation} \begin{split} \frac{S - e^{-r}S_d}{...


3

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 where it is (or higher than strike of your option), you will still end up losing money via premium timing: Even if your bet is correct that eventually stock goes ...


2

There are two main reasons why an institutional trader (or anyone else for that matter) may prefer to short an asset rather than go long on puts. Timing: Shorting gives the trader the ability to cash out of the position whenever they please, whereas a put option may not, depending on its conditions. Risk: Although a put option may magnify the potential ...


3

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 substantial in case someone tries the short squeeze on you, as you could lose your shirt. This is just another example of the black swan biting those who do not really ...


5

We can obtain a closed-form solution for the expected return over an arbitrary holding period under some typical assumptions. Assuming geometric Brownian motion with drift $\mu$ and volatility $\sigma$, the stock price at time $t \geqslant 0$ is $$S(t) = S(0)e^{(\mu - \frac{1}{2}\sigma^2)t}e^{\sigma \sqrt{t} z},$$ where $z \sim \mathcal{N}(0,1)$, a standard ...


4

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 relative to Y, which is too low relative to X. Expressing this view via an options position would implicitly require them to take an additional view about the ...


1

This question reminds me of, many moons ago in a galaxy far far away, the third week of every third month, when the pointyheads who think "vega" is a real word used to start talking about "pin risk" [or "the gamma hammer", if they wanted non-derivative grunts who don't think in Greeks to shut up and listen]. The punchline being ...


9

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 trading options at any significant scale, the underwriter of the option will end up shorting the stock anyway, to cover their own risk. As the price fluctuates, ...


11

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 inception and maturity exceeds the implied volatility of the option (priced in at inception of the option), the option seller would lose money if they delta-...


4

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.


3

It's my understanding that indeed the cross partial derivative terms do have a contribution - so you're correct to say that what u really have to work with is a gamma matrix $$\gamma=[\frac{d^2V}{dr_idr_j}]_{i,j}.$$ In essence, the cross partial terms $\frac{d^2}{dr_idr_j}$ allude to the correlation between the various rates $(r_1,...,r_n)$. Assuming a high (...


1

The option exchanges have a set of general rules for the distance between strikes as well as a fixed schedule for when new expirations are added. When an underlying first begins offering options, in-, at- and out-of-the-money strike prices are initially listed. New strike prices can be added as the underlying index level moves up or down. Addition of new ...


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