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a) $$P_t=100/1.09+(100+1000)/1.09^2=1017,591112$$

So $\sigma^2_TT$ must be strictly increasing to avoid arbitrage. -- For a specific arbitrage portfolio, we would need additional assumptions on the dynamics and type of the option. … This is therefore a riskfree arbitrage profit, if $\sigma^2_TT$ was constant over time. …

Assume the stockprice as in the Black-Scholes model (Geometric Brownian Motion): $$S_t=S_0e^{(\mu-\sigma^2/2)\cdot t+\sigma W_t}$$ Wouldn't there be an immediate arbitrage opportunity, to just buy the … As we know, the Black-Scholes model is assumed to be arbitrage-free with unlimited debt and time horizon. …

No, because the volume does not indicate the price change. E.g. the price change might net to zero over all times.

The fact that one claim has an arbitrage-free price, does not imply that the entire market (for all claims) is arbitrage-free. E.g. $C_T=0$ is always arbitrage-free. …

In this case you actually receive net \$1 option premiums which yields additional interest at maturity: $$+1\cdot e^{rT}$$ Hence the net value is always positive and represents an arbitrage. …

Here an excerpt from my script: Here EMM = Equivalent Martingale Measure (Q), NA = No-Arbitrage. …

If the condition $$0<d<1+r<u$$ is not satisfied, the Binomial model (with $d<u$) would have immediate arbitrage opportunity: 1) $1+r\geq u$: Then the riskfree asset would yield least as much return as … the stock in any state for any probability, so you could short the stock to buy the riskfree asset and end up with some riskless profit with positive probability (arbitrage). 2) $d\geq 1+r$: Then the …

This is not exactly the same as saying there was no arbitrage, because it might be the case that a replicating portfolio does not exist (incomplete market), while the market itself is still arbitrage-free …

Therefore, any market with a riskneutral measure Q is arbitrage-free, and if Q is unique it is also complete. … The riskneutral probabilities $q$ are unique for the binomial model, so it is arbitrage-free and complete. …

In our lecture, we were told to omit the proof because it was too difficult. Maybe it will help you though if you can read it here:

There is no arbitrage opportunity from this predictable jump, because the investors receive the same amount of price depreciation back in cash from the dividend. But how about options? … So isnt there an arbitrage opportunity to short all call before the dividend and buy them back cheaper afterwards? …

If I have a large order to fill, shouldn't I always buy a derivative in the same direction to profit from the market impact? E.g. I sell 1 million shares and so I buy a put, which will hence almost s …

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price process … Why does the existence of Q matter for arbitragefree property, if we have the physical measure P under which there potentially actually is an arbitrage opportunity? …