Valuing Option Credit Spreads

Question

I'm trying to come up with a metric to value and compare spreads. One way that I was doing this was to compute the Expected Value of the spread.

To calculate the expected value I used the following from omnieq

$$ E = C \left(1 - \mathrm{N}\left(d_{2_{s}}\right)\right) - L \cdot \mathrm{N}\left(d_{2_{l}}\right) - \min{\left(\frac{\left|K_{s} - K_{l}\right|}{1 + \frac{\mathrm{N}\left(d_{2_{s}}\right)}{\mathrm{N}\left(d_{2_{l}}\right)}}, L \left(\mathrm{N}\left(d_{2_{s}}\right) - \mathrm{N}\left(d_{2_{l}}\right)\right)\right)} $$

Where

• $S_0$ is the current underlying stock price
• $K$ is the strike price (with $K_s$ being the strike of the short leg and $K_l$ of the long--this is true wherever $s$ and ${l}$ appear in the subscript)
• $\sigma$ is the implied volatility
• $r$ is the risk-free rate
• $T$ is the time to maturity in years
• $q$ is the dividend yield
• $\mathrm{N}\left(x\right)$ is the cumulative distribution function
• $d_1 = \ln\left(\frac{S_0}{K}\right) + \frac{T \left(r - q + \frac{\sigma^2}{2}\right)}{\sigma \sqrt{t}}$
• $d_2 = d_1 - \sigma \sqrt{T}$
• $C$ is the credit received from selling the credit
• $L = \left|K_s-K_l\right|-C$, the max loss of the credit

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So for example, take a current (3/22 AH) SPY credit call spread of

-1 SPY 04/23 0.271∆ $402.50c @ $2.43
+1 SPY 04/23 0.215∆ $405.00c @ $1.77

• The credit for this spread is

$$ $2.43 - $1.77 = $0.66 $$

• The max loss is

$$ \left| $402.50 - $405 \right| - $0.66 = $1.84 $$

• The expected value is

$$ E = $0.66 \cdot \left(1 - 0.271\right) - $1.84 \cdot 0.215 - \\ \min\left({\frac{\left|$402.50 - $405.00\right|}{1+\frac{0.271}{0.215}}, $1.84 \cdot \left(0.271 - 0.215\right)}\right) $$

$$ E = $0.48114 - $0.3956 - \min{\left($1.10596707819,$0.10304\right)} $$

$$ E=-$0.0175 $$

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Using expected value as a metric to compare spreads is OK but not ideal. Namely because if we modify the spread by widening the strikes (in this example and in almost every other example I look at), the increase in max loss dominates the increase in credit and EV goes down.

However, when comparing two credit spreads that are equivalent besides the width of the strikes, the spread with the wider longer strike is more valuable because

1. The break-even point is further OTM, increasing the probability of profit,
2. The exposure to the short leg's greeks is greater, allowing greater theta / greater time decay, and
3. The credit received is greater

Then my question is, what metric can I use to evaluate a credit spread that's dependent on the same variables as the Expected Value as well as the value provided by widening the strikes?

For example, I thought perhaps Expected Value times the spread's net theta might be interesting but this metric still does not recommend widening strikes as I would expect. There must be some modification that can be made such that widening the strikes on the long-side is seen as more valuable than narrowing, up to a point where max loss eventually dominates. Further widening the strikes on the short-side should be seen as making the spread less valuable.

Thanks.