add market valuation functions

[MazyGio]

Resolved Issues

Adds calculate_value_long and calculate_value_short functions as described in #138 (https://github.com/delvtech/hyperdrive-rs/issues/138)

Description

formula for value_long:

market_estimate = trading_proceeds - flat_fees_paid - curve_fees_paid

trading_proceeds = flat_value + curve_value
flat_value       = dy * (1 - t)
curve_bonds      = dy * t
curve_value      = curve_bonds * p
                 = dy * t * p
flat_fees_paid   = flat_value * flat_fee
                 = dy * (1 - t) * flat_fee
curve_fees_paid  = (curve_bonds - curve_value) * curve_fee 
                 = dy * t * (1 - p) * curve_fee

dy = bond amount
p  = spotPrice
t  = termRemaining (positionDuration - (currentTimestamp - openTimestamp))

formula for value_short:

market_estimate = yield_accrued + trading_proceeds - curve_fees_paid + flat_fees_returned

yield_accrued      = dy * (c-c0)/c0
trading_proceeds   = dy * (1 - p) * t
curve_fees_paid    = trading_proceeds * curve_fee
flat_fees_returned = dy * t * flat_fee

dy = bond amount
c  = vaultSharePrice (current if non-matured, or checkpoint's if matured)
c0 = openVaultSharePrice
p  = spotPrice
t  = termRemaining (positionDuration - (currentTimestamp - openTimestamp))

Review Checklists

Please check each item before approving the pull request. While going through the checklist, it is recommended to leave comments on items that are referenced in the checklist to make sure that they are reviewed.

• [ ] Testing
  • [ ] Are there new or updated unit or integration tests?
  • [ ] Do the tests cover the happy paths?
  • [ ] Do the tests cover the unhappy paths?
  • [ ] Are there an adequate number of fuzz tests to ensure that we are covering the full input space?
  • [ ] If matching Solidity behavior, are there differential fuzz tests that ensure that Rust matches Solidity?

[MazyGio]

I'm not sure about how we'd want to write tests for these functions, as they're basically estimates. Any direction is appreciated!

[dpaiton]

I like Mihai's second suggestion, calculate_market_value_* better than calculate_value_*. But that might just be because I'm not native in this field and thus have a preference for more verbose names. Your call in the end.

[MazyGio]

test_calculate_market_value_short passes with a tolerance of 1e12. It's worth noting that the test attempts to close a short of size minimum_transaction_amount (range from 0.1 to 1 bonds).

There's a couple things I've been able to drill down on while testing this function:

1. I've reworked the function to match calculate_close_long as closely as possible. The only difference is now on how both functions calculate the curve part of the trade. This makes up the entire error amount on this test.
2. Using a relatively large liquidity amount (1e27) by doing .calculate_pool_state_after_add_liquidity(fixed!(1e27), true)?; after the initial State is generated does result in a smaller market_impact, but it somehow creates a larger discrepancy between hyperdrive_valuation and spot_valuation. I can't say for certain why that is, but it makes the hyperdrive_valuation result a bit erratic. I'd expect it to be slightly lower than the spot_valuation, since the hyperdrive_valuation considers market impact, but sometimes it's not.

I suspect small rounding-related inaccuracies when computing calculate_shares_in_given_bonds_out_up_safe, made relatively large due to the large share reserve and adjustment levels compared to the small position size.

Example failure using .calculate_pool_state_after_add_liquidity(fixed!(1e27), true)?;:

==========================================
spot_price:       0.073223040957386746
spot_price_after: 0.073223040957595844
market_impact:        209098         <--[O(1e7). very small!]
valuation_error:      11363446861    <--[O(1e11). pretty large]
spot_valuation:       0.111224043778463171
hyperdrive_valuation: 0.111224055141910032    <--[larger than spot, which is weird]
share_reserves:            676920352.732639701955744293
share_adjustment:          -15427047685553773566980402
effective_share_reserves:  692347400.418193475522724695
failed 603 times.    <--[out of 10k]
==========================================
test short::close::tests::test_calculate_market_value_short ... ok

Example failure without that line:

==========================================
spot_price:       0.353913457944902287
spot_price_after: 0.353913875316959714
market_impact:        417372057427   <--[O(1e12)]
valuation_error:      54535898369    <--[O(1e11). Same order of magnitude as above]
spot_valuation:       0.726982046773411663
hyperdrive_valuation: 0.726981992237513294    <--[when it's higher than spot, the error is smaller than 1e10]
share_reserves:            95894096.977191008442078684
share_adjustment:          95886552995656698674111646
effective_share_reserves:  7543.981534309767967038
failed 17 times.    <--[out of 10k]
==========================================

Both tests used a tolerance of 1e10 (to ensure it failed a bunch of times)

3. When I don't use the larger liquidity amount, the error is always within one order of magnitude from the price impact. It's worth noting that, in lieu of a calculate_spot_price_after_close_short function, I've approximated the price impact by using calculate_spot_price_after_long, using the amount of non-matured bonds, which should have a fairly similar effect.

Would we be okay with the tests passing with "large" discrepancies between hyperdrive_valuation and spot_valuation, as long as these discrepancies are e.g. within one or two orders of magnitude of the position's market impact?

[MazyGio]

After reworking these to match their calculate_close_ counterparts, I've tested extensively to figure out a base tolerance, which we can scale depending on the ratio of effective_share_reserves relative to bond_reserves. When this ratio ze / y is too low, it creates a large discrepancy due to the market_impact that affects the hyperdrive valuation, so we bump the base tolerance of 1e12 to 1e13 in such cases.

Thanks @dpaiton for all the help in getting these completed!