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Typically structures like this are traded as notes. They will be sold at a face value of 100%, where that is normally the combination of a zcb (ie 1y usd, say 97.5%), expected coupon (say +10%), short Knock In put (also knocked out by the autocall feature, say -8%), and some profit for the issuer (in this case, 100%-97.5%-10%+8%=0.5%). Sometimes these are ...


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A Heat Rate Call Option, or HRCO as it's commonly known is an example of a class of options known as spread options. Specifically: Intrinsic Value_HRCO = Max(PowerPrice - GasPrice*Heat_Rate - Strike,0).The strike is fixed, and usually consists of items Variable and Operational Maintenance costs (VOM), Start Charge, Start Fuel etc.These are usually fixed and ...


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If you sold the call on the EUR with a strike of USD 1.10, and you did not have the EUR on hand, you would have to buy EUR at market to deliver to the long call holder. You would buy EUR at USD 1.12 and deliver those EUR to the call holder that exercised. You would receive USD 1.10 on exercise so you would lose USD 0.02 per EUR on the exercise. Of ...


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The correct (quant) answer is: the delta depends on the model. If you don't want to calculate the SV or LV or SLV model delta, but like to work within the BSM framework, then the delta to use is $$ \Delta = \Delta^{BS} (\Sigma) + \nu^{BS}(\Sigma) \frac{\partial \Sigma}{\partial S} $$ where $\Delta$ is the skew adjusted delta, $\Delta^{BS} (\Sigma)$ is ...


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Here's a simple way to get the price of the call on the forwards price using risk neutral pricing. Suppose we have a European call that pays at $t = T$, $(For(T,T^*) - K)^+$, where $T^* \geq T$. Further assume interest rates are constant and are represented by "$r$". Let $c^{For}(t, s)$ be the price of the call where $S(t) = s$. Then if the stock pays no ...


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I was one of the floor traders in bond options in the early 80's. Knowledge of options was growing fast at the time primarily lead by the O'Connor brothers who were grain traders from the CBOT. They were the primary force in founding the CBOE. They also developed a large trading operation there in options. When I first started trading bond options most ...


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There are two ways to look at it, a mathematical way or an alternative, intuitive way. The alternative way can be to look at F as an alternative S with 0 interest rate discounting because we still have the cash (minus a small posted margin, and ignoring this) which earns the interest rate. So for the F’s value itself every day’s time value of money effect ...


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Put-Call Parity $C - P = S - K*e^{-rt}$ provided the implied volatility of $C$ and $P$ are the same. If the implied volatilities are different, there could be arbitrage taking opportunities exist. However, it doesn't mean there must be an arbitrage opportunity. If the implied volatilities being different doesn't result in arbitrage opportunity, then the ...


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Yes, matching by strike, expiry and valuation date makes total sense. My guess is that you're only getting valuations for options that have valuations, ie options that have been written. Or at least against which the dealers have bothered to offer quotes. In which case, I suspect the mismatch you're getting is lots of calls with high strikes that have no ...


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If you exercise the option (assuming that is an american option) you would receive the intrinsic value, which is for a Call option $\max(S-K, 0) $, and for a Put option $\max(K-S, 0)$. Hence, 11300.00 - 11100.00 = 200. If you are talking about selling the option instead of exercising it, I recommend to have a look at the Black & Scholes model, John C ...


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Taleb argues that under uncertainty, election forecasts should be seen as a Binary option. A similar thought is presented by De Finetti's principle that probability should be treated like a two-way "choice" price. Therefore, under high levels of volatility, forecast should not have extreme variation across time (equivalently, the price of the binary option ...


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It is simpler than the other Greeks, and the reason you don't hear a lot about $\rho$ is because it has smaller impact in the scheme of things. Let's say we are in the BS world, then the rho formulae for a call or put are rather simple: $\rho_{\mathrm{Call}} = K { e^{- r_{d} \tau} }\tau { N\left (d_{2} \right ) }$ $\rho_{\mathrm{Put}} = - K { e^{- r_{d}...


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Apologies upfront if my Finance is better than my grasp on the finer points of advanced calculus. I know the argument(s) he's making; and just hope someone more Quant than I can land the point home. He's arguing that a "simple" bet and a binary option, which is an "exotic" option, are one and the same thing! Which is true. Both end up worth 0 or 1, versus ...


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"Liquidity" has (at least) three different meanings here. They're all obviously interconnected market impact: what is my ability to trade in this market without people noticing, and that moving the price? This is chiefly a function of depth, so open interest looms large. If there's X gross contracts already out there, then the market won't notice my new ...


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Theoretically, it's "complicated". Build a spreadsheet of all the index constituents, their expected payouts, associated dates, and real-time stock prices, and index weights. Then hours of struggle later, cross your fingers, and hope you haven't made any calculation mistakes ;-) The quick and easy way... simplify your equations with r=0 and replace the spot ...


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You need to hedge dynamically (ie, with changes in IV/delta) to accurately hedge your position. This also winds up being a potential risk for a covered option position if there are big moves or general lack of liquidity, since it can be more difficult and also more important to hedge at those times given large market moves.


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This article discusses the topic well, you can model the short term discrete dividends from discrete fixed and the medium/long term with discrete proportional dividends. If you know the annual estimated dividend (Factset estimates/dividend swaps etc), you can use historical payment amounts and dates to weight and project the discrete fixed dividends and then ...


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I will try to be as concise as possible. For obvious reasons, if you do not have any trades, choose the quotes, because they reflect the intention of a player to trade at that level of price/implied_vol at a certain point in time (where we have no trades because those quotes are not matched by other traders). If instead you have a quote and a trade ...


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It's a little dependent on whether its listed or otc options but your question about implied volatilities probably addresses the issue the best. I would calculate the implied volatility from the real transactions noting whether its a buy or sell and then do the same for the markets that you are seeing and compare them depending on what the market has done ...


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To make this clear. The article considers a bond that is paying a coupon infinitely, so there is no expiration. In this case, the value of the bond is the sum of the discounted coupons $\frac{100}{(1+r)}+\frac{100}{(1+r)^2}+\frac{100}{(1+r)^3}+\dots$ which eqals $\frac{100}{r}$. So in case of $r=0.10$ the bond price is $\frac{100}{0.1}=1000$ and in case of $...


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Answer was provided to me in the comments so I may as well close the question non. My computation is right, and the Investopedia article is not saying what I thought it was. (What the article really says is still unclear.)


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I can confirm there is no error in @Sanjay graph. I obtain the same plot with Obloj correction for the SABR formula. In fact, the popular SABR approximation formulas (Hagan or the further corrections) use as hypothesis a small vol of vol. In your case, the vol of vol $\nu$ is very large ($\nu=7$) and it is not too surprising that the approximations break ...


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First, VRP is (loosely speaking) the difference between the implied and objective variance of future returns: $VRP_t = Var_t^P[R_{t+1}] - Var_t^Q[R_{t+1}]$, of which only the second, risk-neutral variance is observed at time $t$. Assuming that (1) investors have been correct on average about the future variance, and that (2) the premium is stationary, one ...


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You got to be careful with $\mathbb{P}$ and $\mathbb{Q}$. Indeed, $N(d_2)$ is the probability of the event $\{S_T\geq K\}$ in the risk-neutral world. Note that $r$ (or $r-q$) is the drift in the risk-neutral world and hence this variable occurs in $d_2$. Since time to maturity and volatility are typically small numbers, i.e. $d_1=d_2+\sigma\sqrt{T-t}\approx ...


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Keeping it simple, your payoff at time t is: $S_t-100$ The present value of the stock is $S_0$, it’s current price; and the present value of 100 is its discounted value as you correctly explained in your question.


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Somewhere must be a little error, here I used $r=0.02$ and $\sigma=0.25$. In black you have the payoff and in red the current price of the portfolio. Note that as the time to maturity decreases, the red line converges towards the black line. In grey and and yellow (on the secondary axis), you can see the individual call option prices which form your ...


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