Say, an investment bank sell Digital Call Option to its client at strike 100. But trader at the bank want to book the deal with a call spread at 99/100 (price&hedge Digital Option like price&hedge a call spread) because trader believe that it will help smoothing hedging.

How should risk manager at the bank measure the risk?

  1. a digital option as it is an actual contingent obligation?

  2. or a call spread as it is what trader book the deal?

  • 2
    $\begingroup$ Risks and hedging go along, both should be based on what is actually in the books (here the call spread). Actually this call-spread 99/100 cost more than the digital feature you're selling to your client, so it could be seen as digital + margin. $\endgroup$ – Quantuple Feb 10 '17 at 8:39
  • $\begingroup$ @Quantuple Does this work other way around, if client instead writes Digital Option, bank will pay more (-margin) if bank book digital option as call spread? $\endgroup$ – Jack JackGuRae Feb 10 '17 at 8:45
  • $\begingroup$ It's always the same. You book what you buy/sell. Then the prices and hedges are determined based on your in house models. The idea being that you should incorporate a margin to your price, margin that you'll try to defend by hedging properly. Although it's a pretty long read I suggest you have a look at papers.ssrn.com/sol3/papers.cfm?abstract_id=2365294 $\endgroup$ – Quantuple Feb 10 '17 at 9:13
  • $\begingroup$ @jackgurae, If client sells the digital , you book a 100-101 call spread. $\endgroup$ – dm63 Feb 11 '17 at 12:12
  • $\begingroup$ What if strike of digital is at 26.76. Payoff is either 1 or nothig. Given that tick size around this price range is 0.25. How would I set up a call spread? 26.50/26.76 would require about 4x leverage (buy at 26.50 and sell at 26.76). But in practice I can use only 2x leverage (buy at 26.50 and sell at 27.00) $\endgroup$ – Jack JackGuRae Feb 23 '17 at 8:04

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